" {font "name,size"} {tc <colorspec>}} {lt <linetype>} {fs <fillstyle>} {at <x-coord>} More than one set of histograms can appear in a single plot. In this case you can force a gap between them, and a separate label for each set, by using the `newhistogram` command. For example set style histogram cluster plot newhistogram "Set A", 'a' using 1, '' using 2, '' using 3, \ newhistogram "Set B", 'b' using 1, '' using 2, '' using 3 The labels "Set A" and "Set B" will appear beneath the respective sets of histograms, under the overall x axis label. The newhistogram command can also be used to force histogram coloring to begin with a specific color (linetype). By default colors will continue to increment successively even across histogram boundaries. Here is an example using the same coloring for multiple histograms plot newhistogram "Set A" lt 4, 'a' using 1, '' using 2, '' using 3, \ newhistogram "Set B" lt 4, 'b' using 1, '' using 2, '' using 3 Similarly you can force the next histogram to begin with a specified fillstyle. If the fillstyle is set to `pattern`, then the pattern used for filling will be incremented automatically. Starting a new histogram will normally add a blank entry to the key, so that titles from this set of histogram components will be separated from those of the previous histogram. This blank line may be undesirable if the components have no individual titles. It can be suppressed by modifying the style with `set style histogram nokeyseparators`. Ffigure_newhist The `at <x-coord>` option sets the x coordinate position of the following histogram to <x-coord>. For example set style histogram cluster set style data histogram set style fill solid 1.0 border -1 set xtic 1 offset character 0,0.3 plot newhistogram "Set A", \ 'file.dat' u 1 t 1, '' u 2 t 2, \ newhistogram "Set B" at 8, \ 'file.dat' u 2 t 2, '' u 2 t 2 will position the second histogram to start at x=8. 3 automated iteration over multiple columns ?automated ?with histograms automated ?histograms automated ?styles histograms automated ?plotting styles histograms automated If you want to create a histogram from many columns of data in a single file, it is very convenient to use the plot iteration feature. See `plot for`. For example, to create stacked histograms of the data in columns 3 through 8 set style histogram columnstacked plot for [i=3:8] "datafile" using i title columnhead 3 histogram color assignments ?with histograms colors ?histograms colors ?styles histograms colors ?plotting styles histograms colors The program assigns a color to each component box in a histogram automatically such that equivalent data values maintain a consistent color wherever they appear in the rows or columns of the histogram. The colors are taken from successive linetypes, starting either with the next unused linetype or an initial linetype provided in a `newhistogram` element. In some cases this mechanism fails due to data sources that are not truly parallel (i.e. some files contain incomplete data). In other cases there may be additional properties of the data that could be visualized by, say, varying the intensity or saturation of their base color. As an alternative to the automatic color assignment, you can provide an explicit color value for each data value in a second `using` column via the `linecolor variable` or `rgb variable` mechanism. See `colorspec`. Depending on the layout of your data, the color category might correspond to a row header or a column header or a data column. Note that you will probably have to customize the key sample colors to match (see `keyentry`). Example: Suppose file_001.dat through file_008.dat contain one column with a category identifier A, B, C, ... and a second column with a data value. Not all of the files contain a line for every category, so they are not truly parallel. The program would be wrong to assign the same color to the value from line N in each file. Instead we assign a color based on the category in column 1. file(i) = sprintf("file_%03d.dat",i) array Category = ["A", "B", "C", "D", "E", "F"] color(c) = index(Category, strcol(c)) set style data histogram plot for [i=1:8] file(i) using 2:(color(1)) linecolor variable A more complete example including generation of a custom key is in the demo collection ^ <a href="https://www.apklas.com?arsae=http%3A%2F%2Fwww.gnuplot.info%2Fdemo%2Fhistogram_colors.html" target="_parent"> histogram_colors.dem ^ </a> D histogram_colors 1 2 hsteps ?plotting styles hsteps ?style hsteps ?with hsteps ?hsteps The 2D plotting style `with hsteps` renders a horizontal line segment ("step") for each data point. The step may extend to the left, to the right, or to both sides of the point's x-coordinate. Additional keywords control the lines connecting adjacent steps and option area fill between the step and a baseline y value. Syntax: plot <data> with hsteps {forward|backward} {baseline|pillars|link|nolink} {{above|below} y=<baseline>} {offset <y-offset>} 2 columns: x y 3 columns: x y width This plot style requires 2 or 3 columns of data. Additional input columns can be used to provide variable line or fill colors (see `rgbcolor variable`). The x values of the input data are assumed to be monotonic. If the width of each step is not explicitly given through a third input column, each segmentâ€™s width is calculated so that it abuts the adjacent horizontal segments. A negative value in column 3 will be treated as a request for a full-width step. The `forward` and `backward` keywords can be used to specify the direction in which the horizontal segment extends from the given x coordinate. If neither is specified, the horizontal segment extends on both sides of the given x-value halfway to the x-value of the next adjacent point. However, for the first and last points, where there are no corresponding outer adjacent points, the horizontal segments are extrapolated using distances to the adjacent inner points (see `histeps`, `boxes`). The default (`baseline`) and `pillar` variants employ a baseline y value. If not provided in the plot command, the baseline is taken to be y=0. If the plot command uses a fill style, the baseline also serves to delimit one boundary of the fill area. Four style variants are possible. Ffigure_hsteps_baseline `baseline` (default): If there is no gap along x between adjacent steps, they are connected by a vertical line segment between them. This produces a curve like the `steps`, `histeps`, or `fsteps` styles. If there is a gap between steps, usually because the width is less than the point spacing, the connecting line drops to the baseline and continues along it before rising again. This produces a sequence of rectangular pulses. set xzeroaxis plot $data using 1:2 with hsteps plot $data using 1:2:(0.5) with hsteps Ffigure_hsteps_pillar `pillar`: At each end of each step a vertical line is drawn to the baseline. Note that no horizontal line segments are drawn at the baseline. plot $data using 1:2 with hsteps pillar plot $data using 1:2:(0.5) with hsteps pillar plot $data using 1:2:(0.5) \ with hsteps pillar above fc "blue", \ $data using 1:2:(0.5) \ with hsteps pillar below fc "red" #TeX \vspace{6ex} Ffigure_hsteps_nolink `nolink`: No connecting line is drawn between adjacent steps. Baseline and fill properties are not relevant to this variant. plot $data using 1:2 with hsteps nolink, \ $data using 1:2 with hsteps nolink forward, \ $data using 1:2 with hsteps nolink backward, \ $data using 1:2 with points pt "|" #TeX \vspace{9ex} Ffigure_hsteps_link `link`: Adjacent steps steps are connected by a single straight line segment. Depending on the step widths, this line may be diagonal rather than vertical. Example: The `link` variant can be superimposed onto the `pillar` variant to produce a stacked histogram plot in which category boundaries are connected. set style line 11 lw 2 lc "gray" dt "." set style line 12 lw 2 lc variable plot $data using 1:3:(0.5) ls 11 with hsteps link, \ $data using 1:3:(0.5):1 ls 12 with hsteps pillar fs solid 0.7 border, \ $data using 1:4:(0.5) ls 11 with hsteps link, \ $data using 1:4:(0.5):1 ls 12 with hsteps pillar fs transparent pattern 1 border 3 offset Ffigure_hsteps_offset ?with hsteps offset ?hsteps offset The offset value modifies any of the `with hsteps` variants by adding an increment to the y value of both the data point itself (column 2) and the baseline of the plot it appears in. An example of use is to draw a logic circuit timing chart in which pulse waveforms are aligned vertically. In general the offset can be used to stack plots from multiple data sets that share a common range of y values. # bit(k,char) is a function that returns 0 or 1 # for the state of bit k in an ASCII character set style fill solid 0.2 border plot for [k=1:8] STR using 1:(bit(k,STR[$1])):(0.5) \ with hsteps fillcolor "black" offset k 3 missing data ?with hsteps missing-data ?hsteps missing-data In the hsteps style, empty lines, NaN values, and missing data have distinct meanings. If an empty line is present in the data, the data series is reset at that point. This is analogous to a blank line causing a break to start a new curve in the case of `with lines`. If an x-value contains NaN, it is processed in the same manner as an empty line. If the x-value is valid but the y-value contains NaN, no horizontal line is drawn for that particular data point but the x-value is still used if needed to estimate the step width. 2 image ?plotting styles image ?style image ?with image ?image ?rgbimage ?rgbalpha The `image`, `rgbimage`, and `rgbalpha` plotting styles all project a uniformly sampled grid of data values onto a plane in either 2D or 3D. The input data may be an actual bitmapped image, perhaps converted from a standard format such as PNG, or a simple array of numerical values. These plot styles are often used to produce heatmaps. For 2D heatmaps in polar coordinates, see `set polar grid`. Ffigure_heatmap This figure illustrates generation of a heat map from an array of scalar values. The current palette is used to map each value onto the color assigned to the corresponding pixel. See also `sparse`. plot '-' matrix with image 5 4 3 1 0 2 2 0 0 1 0 0 0 1 0 0 1 2 4 3 e e Ffigure_rgb3D Each pixel (data point) of the input 2D image will become a rectangle or parallelepiped in the plot. The coordinates of each data point will determine the center of the parallelepiped. That is, an M x N set of data will form an image with M x N pixels. This is different from the pm3d plotting style, where an M x N set of data will form a surface of (M-1) x (N-1) elements. The scan directions for a binary image data grid can be further controlled by additional keywords. See `binary keywords flipx`, `keywords center`, and `keywords rotate`. Ffigure_scaled_image Image data can be scaled to fill a particular rectangle within a 2D plot coordinate system by specifying the x and y extent of each pixel. See `binary keywords dx` and `dy`. To generate the figure at the right, the same input image was placed multiple times, each with a specified dx, dy, and origin. The input PNG image of a building is 50x128 pixels. The tall building was drawn by mapping this using `dx=0.5 dy=1.5`. The short building used a mapping `dx=0.5 dy=0.35`. The `image` style handles input pixels containing a grayscale or color palette value. Thus 2D plots (`plot` command) require 3 columns of data (x,y,value), while 3D plots (`splot` command) require 4 columns of data (x,y,z,value). The `rgbimage` style handles input pixels that are described by three separate values for the red, green, and blue components. Thus 5D data (x,y,r,g,b) is needed for `plot` and 6D data (x,y,z,r,g,b) for `splot`. The individual red, green, and blue components are assumed to lie in the range [0:255]. This matches the convention used in PNG and JPEG files (see `binary filetype`). However some data files use an alternative convention in which RGB components are floating point values in the range [0:1]. To use the `rgbimage` style with such data, first use the command `set rgbmax 1.0`. =alpha channel The `rgbalpha` style handles input pixels that contain alpha channel (transparency) information in addition to the red, green, and blue components. Thus 6D data (x,y,r,g,b,a) is needed for `plot` and 7D data (x,y,z,r,g,b,a) for `splot`. The r, g, b, and alpha components are assumed to lie in the range [0:255]. To plot data for which RGBA components are floating point values in the range [0:1], first use the command `set rgbmax 1.0`. If only a single data column is provided for the color components of either rgbimage or rgbalpha plots, it is interpreted as containing 32 bit packed ARGB data using the convention that alpha=0 means opaque and alpha=255 means fully transparent. Note that this is backwards from the alpha convention if alpha is supplied in a separate column, but matches the ARGB packing convention for individual commands to set color. See `colorspec`. 3 transparency ?image transparency ?transparency ?alpha channel The `rgbalpha` plotting style assumes that each pixel of input data contains an alpha value in the range [0:255]. A pixel with alpha = 0 is purely transparent and does not alter the underlying contents of the plot. A pixel with alpha = 255 is purely opaque. All terminal types can handle these two extreme cases. A pixel with 0 < alpha < 255 is partially transparent. Terminal types that do not support partial transparency will round this value to 0 or 255. D argb_hexdata 2 3 image pixels ?plotting styles image pixels ?style image pixels ?with image pixels ?image pixels ?pixels =heatmaps Some terminals use device- or library-specific optimizations to render image data within a rectangular 2D area. This sometimes produces undesirable output, e.g. inter-pixel smoothing, bad clipping or missing edges. An example of this is the smoothing applied by web browsers when rendering svg images. The `pixels` keyword tells gnuplot to use generic code to render the image pixel-by-pixel. This rendering mode is slower and may result in larger output files, but should produce a consistent rendered view on all terminals. It may in particular be preferable for heatmaps with a small number of pixels. Example: plot 'data' with image pixels 2 impulses ?plotting styles impulses ?style impulses ?with impulses ?impulses Ffigure_impulses The `impulses` style displays a vertical line from y=0 to the y value of each point (2D) or from z=0 to the z value of each point (3D). Note that the y or z values may be negative. Data from additional columns can be used to control the color of each impulse. To use this style effectively in 3D plots, it is useful to choose thick lines (linewidth > 1). This approximates a 3D bar chart. 1 column: y 2 columns: x y # line from [x,0] to [x,y] (2D) 3 columns: x y z # line from [x,y,0] to [x,y,z] (3D) 2 labels ?plotting styles labels ?style labels ?with labels ?labels Ffigure_labels1 The `labels` style reads coordinates and text from a data file and places the text string at the corresponding 2D or 3D position. 3 or 4 input columns of basic data are required. Additional input columns may be used to provide properties that vary point by point such as text rotation angle (keywords `rotate variable`) or color (see `textcolor variable`). 3 columns: x y string # 2D version 4 columns: x y z string # 3D version The font, color, rotation angle and other properties of the printed text may be specified as additional command options (see `set label`). The example below generates a 2D plot with text labels constructed from the city whose name is taken from column 1 of the input file, and whose geographic coordinates are in columns 4 and 5. The font size is calculated from the value in column 3, in this case the population. CityName(String,Size) = sprintf("{/=%d %s}", Scale(Size), String) plot 'cities.dat' using 5:4:(CityName(stringcolumn(1),$3)) with labels If we did not want to adjust the font size to a different size for each city name, the command would be much simpler: plot 'cities.dat' using 5:4:1 with labels font "Times,8" If the labels are marked as `hypertext` then the text only appears if the mouse is hovering over the corresponding anchor point. See `hypertext`. In this case you must enable the label's `point` attribute so that there is a point to act as the hypertext anchor: plot 'cities.dat' using 5:4:1 with labels hypertext point pt 7 Ffigure_labels2 The `labels` style can also be used in place of the `points` style when the set of predefined point symbols is not suitable or not sufficiently flexible. For example, here we define a set of chosen single-character symbols and assign one of them to each point in a plot based on the value in data column 3: set encoding utf8 symbol(z) = "âˆ™â–¡+âŠ™â™ â™£â™¡â™¢"[int(z):int(z)] splot 'file' using 1:2:(symbol($3)) with labels This example shows use of labels with variable rotation angle in column 4 and textcolor ("tc") in column 5. Note that variable color is always taken from the last column in the `using` specifier. plot $Data using 1:2:3:4:5 with labels tc variable rotate variable 2 lines ?plotting styles lines ?style lines ?with lines ?lines Ffigure_lines The `lines` style connects adjacent points with straight line segments. It may be used in either 2D or 3D plots. The basic form requires 1, 2, or 3 columns of input data. Additional input columns may be used to provide information such as variable line color (see `rgbcolor variable`). 2D form (no "using" spec) 1 column: y # implicit x from row number 2 columns: x y 3D form (no "using" spec) 1 column: z # implicit x from row, y from index 3 columns: x y z See also `linetypes`, `linewidth`, and `linestyle`. 2 linespoints ?plotting styles linespoints ?style linespoints ?with linespoints ?style lp ?with lp ?linespoints ?lp ?pointinterval ?pointnumber Ffigure_linespoints The `linespoints` style (short form `lp`) connects adjacent points with straight line segments and then goes back to draw a small symbol at each point. Points are drawn with the default size determined by `set pointsize` unless a specific point size is given in the plot command or a variable point size is provided in an additional column of input data. Additional input columns may also be used to provide information such as variable line color. See `lines` and `points`. Two keywords control whether or not every point in the plot is marked with a symbol, `pointinterval` (short form `pi`) and `pointnumber` (short form `pn`). `pi N` or `pi -N` tells gnuplot to only place a symbol on every Nth point. A negative value for N will erase the portion of line segment that passes underneath the symbol. The size of the erased portion is controlled by `set pointintervalbox`. `pn N` or `pn -N` tells gnuplot to label only N of the data points, evenly spaced over the data set. As with `pi`, a negative value for N will erase the portion of line segment that passes underneath the symbol. 2 masking ?plotting styles mask ?plot with mask ?with mask ?masking The plotting style `with mask` is used to define a masking region that can be applied to pm3d surfaces or to images specified later in the same `plot` or `splot` command. Input data is interpreted as a stream of [x,y] or [x,y,z] coordinates defining the vertices of one or more polygons. As in plotting style `with polygons`, polygons are separated by a blank line. If the mask is part of a 3D (splot) command then a column of z values is required on input but is currently not used for anything. If a mask definition is present in the plot command, then any subsequent image or pm3d surface in the same command can be masked by adding the keyword `mask`. If no mask has been defined, this keyword is ignored. This example illustrates using the convex hull circumscribing a set of points to mask the corresponding region of a pm3d surface. Ffigure_mask ^<p align="center"><picture> ^ <source srcset="figure_mask.webp" type="image/webp"> ^ <img src="figure_mask.png" alt="figure_mask"> ^ </source></picture></p><p> set table $HULL plot $POINTS using 1:2 convexhull unset table set view map set multiplot layout 1,2 splot $POINTS using 1:2:3 with pm3d, \ $POINTS using 1:2:(0) nogrid with points splot $HULL using 1:2:(0) with mask, \ $POINTS using 1:2:3 mask with pm3d unset multiplot The `splot` command for the first panel renders the unmasked surface created by dgrid3d from the original points and then the points themselves, in that order. The `splot` command for the second panel renders the masked surface. Note that definition of the mask must come first (plot `with mask`), followed by the pm3d surface it applies to (plot style `with pm3d` modified by the `mask` keyword). A more complete version of this example is in the demo collection ^ <a href="https://www.apklas.com?arsae=http%3A%2F%2Fwww.gnuplot.info%2Fdemo%2Fmask_pm3d.html" target="_parent"> mask_pm3d.dem ^ </a> Although it is not shown here, a single mask can include multiple polygonal regions. The masking commands are EXPERIMENTAL. Details may change in a future release. 2 parallelaxes Ffigure_parallel ?plotting styles parallelaxes ?plot with parallelaxes ?with parallelaxes ?parallelaxes ?parallel Parallel axis plots can highlight correlation in a multidimensional data set. Individual columns of input data are each associated with a separately scaled vertical axis. If all columns are drawn from a single file then each line on the plot represents values from a single row of data in that file. It is common to use some discrete categorization to assign line colors, allowing visual exploration of the correlation between this categorization and the axis dimensions. Syntax: set style data parallelaxes plot $DATA using col1{:varcol1} {at <xpos>} {<line properties using col2 ... change: version of gnuplot introduced a change in the syntax for plot style parallelaxes. revised allows an unlimited number parallel axes. with parallelaxes col new also explicit placement vertical axes along x axis as example below. if no coordinate is provide n will be placed at array xpos by default automatically determine range and scale individual from input data but usual commands can used to customize this. see paxis polar plots="polar" ffigure_polar are generated changing current system before issuing command. option tells interpret coordinates>,<radius> rather than <x>,<y>. Many, but not all, of the 2D plotting styles work in polar mode. The figure shows a combination of plot styles `lines` and `filledcurves`. See `set polar`, `set rrange`, `set size square`, `set theta`, `set ttics`. ?polar heatmap Polar heatmaps can be generated using plot style `with surface` together with `set polar grid`. Ffigure_polar_grid set size square set angle degrees set rtics set grid polar set palette cubehelix negative gamma 0.8 set polar grid gauss kdensity scale 35 set polar grid theta [0:190] plot DATA with surface, DATA with points pt 7 2 points ?plotting styles points ?style points ?with points ?points ?point type ?pointtype Ffigure_points The `points` style displays a small symbol at each point. The command `set pointsize` may be used to change the default size of all points. The point type defaults to that of the linetype. See `linetypes`. If no `using` spec is found in the plot command, input data columns are interpreted implicitly in the order x y pointsize pointtype color Any columns beyond the first two (x and y) are optional; they correspond to additional plot properties `pointsize variable`, `pointtype variable`, etc. The first 8 point types are shared by all terminals. Individual terminals may provide a much larger number of distinct point types. Use the `test` command to show what is provided by the current terminal settings. Alternatively any single printable character may be given instead of a numerical point type, as in the example below. You may use any unicode character as the pointtype (assumes utf8 support). See `escape sequences`. Longer strings may be plotted using plot style `labels` rather than `points`. plot f(x) with points pt "#" plot d(x) with points pt "\U+2299" ?points variable ?with points variable =variable ?variable ?pointtype variable ?pointsize variable When using the keywords `pointtype`, `pointsize`, or `linecolor` in a plot command, the additional keyword `variable` may be given instead of a number. In this case the corresponding properties of each point are assigned by additional columns of input data. Variable pointsize is always taken from the first additional column provided in a `using` spec. Variable color is always taken from the last additional column. See `colorspec`. If all three properties are specified for each point, the order of input data columns is thus plot DATA using x:y:pointsize:pointtype:color \ with points lc variable pt variable ps variable Note: for information on user-defined program variables, see `variables`. 2 polygons ?plotting styles polygons ?style polygons ?with polygons ?polygons 2D plots: plot DATA {using 1:2} with polygons `plot with polygons` is currently treated as `plot with filledcurves closed`. Each polygon may be assigned a separate color by providing a third using specifier and the keywords `lc variable` (value is interpreted as a linetype) or `lc rgb variable` (value is interpreted as a 24-bit RGB color). Only the color value from the first vertex of the polygon is used. The border line type, if any, is taken from the fill style. 3D plots: splot DATA {using x:y:z} with polygons {fillstyle <fillstyle spec>} {fillcolor <colorspec>} `splot with polygons` uses pm3d to render individual triangles, quadrangles, and larger polygons in 3D. These may be facets of a 3D surface or isolated shapes. The code assumes that the vertices lie in a plane. Vertices defining individual polygons are read from successive records of the input file. A blank line separates one polygon from the next. The fill style and color may be specified in the splot command, otherwise the global fillstyle from `set style fill` is used. Due to limitations in the pm3d code, a single border line style from `set pm3d border` is applied to all 3D polygons. This restriction may be removed in a later gnuplot version. Each polygon may be assigned a separate RGB color by providing a fourth using specifier and the keywords `lc variable` (value is interpreted as a linetype) or `lc rgb variable` (value is interpreted as a 24-bit RGB color). Only the color value from the first vertex of the polygon is used. pm3d sort order and lighting are applied to the faces. It is probably always desirable to use `set pm3d depthorder`. Ffigure_polygons set xyplane at 0 set view equal xyz unset border unset tics set pm3d depth set pm3d border lc "black" lw 1.5 splot 'icosahedron.dat' with polygons \ fs transparent solid 0.8 fc bgnd 2 rgbalpha ?plotting styles rgbalpha ?style rgbalpha ?with rgbalpha See `image`. 2 rgbimage ?plotting styles rgbimage ?style rgbimage ?with rgbimage See `image`. 2 sectors ?plotting styles sectors ?with sectors ?sectors ?windrose Ffigure_sector_definition The 2D plotting style `with sectors` renders one annular segment ("sector") for each line of input data. The shape of each sector is described by four required data values. An additional pair of data values can be included to specify the origin of the annulus this sector is taken from. A per-sector color may be provided in an additional column. The plot style itself can be used in either cartesian or polar mode (`set polar`). The units and interpretation for the azimuth and the sector angle are controlled using `set angles` and `set theta`. Columns 1 and 2 specify the azimuth (theta) and radius (r) of one corner of the sector. #TeX \newline Columns 3 and 4 specify the angular and radial extents of the sector ("sector_angle" and "annular_width"). #TeX \newline Columns 5 and 6, if present, specify the coordinates of the center of the annulus (default [0,0]). The interpretation is [x,y] in cartesian mode and [theta,r] in polar mode. Syntax: plot DATA {using specifier} {units xy | units xx | units yy} using specifier 4 columns: azimuth radius sector_angle annular_width 5 columns: azimuth radius sector_angle annular_width color 6 columnd: azimuth radius sector_angle annular_width center_x center_y 7 columns: azimuth radius sector_angle annular_width center_x center_y color Note that if the x and y axis scales are not equal, the envelope of the full annulus in x/y coordinates will appear as an ellipse rather than a circle. The annulus envelope and thus the apparent sector annular width can be adjusted to correct for unequal axis scales using the same mechanism as for ellipses. Adding `units xx` to the command line causes the sector to be rendered as if the current x axis scale applied equally to both x and y. Similarly `units yy` causes the sector to be rendered as if the current y axis scale applied equally to both x and y. See `set isotropic`, `set style ellipse`. Ffigure_windrose Plotting with sectors can provide polar coordinate equivalents for the cartesian plot styles `boxes` (see wind rose figure), `boxxyerror` and `image pixels` (see example in `heatmaps`). Because sector plots are compatible with cartesian mode plot layout, multiple plots can be placed at different places on a single graph, which would not be possible for other polar mode plot styles. An example of using sectors to create a wind rose in shown here. Other applications include polar heatmaps, dial charts, pie/donut charts, and annular error boxes for data points in polar coordinates. Worked examples for all of these are given in the ^ <a href="https://www.apklas.com?arsae=http%3A%2F%2Fwww.gnuplot.info%2Fdemo%2Fsectors.html" target="_parent"> sectors demo. ^ </a> 2 spiderplot ?plotting styles spiderplot ?with spiderplot ?spiderplot ?radar chart Spider plots are essentially parallel axis plots in which the axes are arranged radially rather than vertically. Such plots are sometimes called `radar charts`. In gnuplot this requires working within a coordinate system established by the command `set spiderplot`, analogous to `set polar` except that the angular coordinate is determined implicitly by the parallel axis number. The appearance, labelling, and tic placement of the axes is controlled by `set paxis`. Further style choices are controlled using `set style spiderplot`, `set grid`, and the individual components of the plot command. Because each spider plot corresponds to a row of data rather than a column, it would make no sense to generate key entry titles in the normal way. Instead, if a plot component contains a title the text is used to label the corresponding axis. This overrides any previous `set paxis n label "Foo"`. To place a title in the key, you can either use a separate `keyentry` command or extract text from a column in the input file with the `key(column)` using specifier. See `keyentry`, `using key`. In this figure a spiderplot with 5 axes is used to compare multiple entities that are each characterized by five scores. Each line (row) in $DATA generates a new polygon on the plot. Ffigure_spiderplot $DATA << EOD A B C D E F George 15 75 20 43 90 50 Harriet 40 40 40 60 30 50 EOD set spiderplot set style spiderplot fs transparent solid 0.2 border set for [p=1:5] paxis p range [0:100] set for [p=2:5] paxis p tics format "" set paxis 1 tics font ",9" set for [p=1:5] paxis p label sprintf("Score %d",p) set grid spiderplot plot for [i=1:5] $DATA using i:key(1) 3 newspiderplot ?newspiderplot ?spiderplot newspiderplot Normally the sequential elements of a plot command `with spiderplot` each correspond to one vertex of a single polygon. In order to describe multiple polygons in the same plot command, they must be separated by `newspiderplot`. Example: # One polygon with 10 vertices plot for [i=1:5] 'A' using i, for [j=1:5] 'B' using j # Two polygons with 5 vertices plot for [i=1:5] 'A' using i, newspiderplot, for [j=1:5] 'B' using j 2 steps ?plotting styles steps ?style steps ?with steps ?steps Ffigure_steps The `steps` style is only relevant to 2D plotting. It connects consecutive points with two line segments: the first from (x1,y1) to (x2,y1) and the second from (x2,y1) to (x2,y2). The input column requires are the same as for plot styles `lines` and `points`. The difference between `fsteps` and `steps` is that `fsteps` traces first the change in y and then the change in x. `steps` traces first the change in x and then the change in y. To fill the area between the curve and the baseline at y=0, use `fillsteps`. See also ^ <a href="https://www.apklas.com?arsae=http%3A%2F%2Fwww.gnuplot.info%2Fdemo%2Fsteps.html" target="_parent"> steps demo. ^ </a> 2 surface ?plotting styles surface ?style surface ?with surface The plot style `with surface` has two uses. In 3D plots, `with surface` always produces a surface. If a 3D data set is recognizable as a mesh (grid) then by default the program implicitly treats the plot style `with lines` as requesting a gridded surface, making `with lines` a synonym for `with surface`. However the command `set surface explicit` suppresses this treatment, in which case `with surface` and `with lines` become distinct styles that may be used in the same plot. If you have points in 3D that are not recognized as a grid, you may be able to fit a suitable grid first. See `set dgrid3d`. In 2D polar mode plots, `with surface` is used to produce a solid fill gridded represention of the data. Generation of the surface is controlled using the command `set polar grid`. 2 vectors ?plotting styles vectors ?style vectors ?with vectors ?vectors Ffigure_vectors The 2D `vectors` style draws a vector from (x,y) to (x+xdelta,y+ydelta). The 3D `vectors` style is similar, but requires six columns of basic data. In both cases, an additional input column (5th in 2D, 7th in 3D) may be used to provide variable (per-datapoint) color information. (see `linecolor` and `rgbcolor variable`). A small arrowhead is drawn at the end of each vector. 4 columns: x y xdelta ydelta 6 columns: x y z xdelta ydelta zdelta The keywords "with vectors" may be followed by inline arrow style properties, by reference to a predefined arrow style, or by a request to read the index of the desired arrow style for each vector from a separate input column. See the first three examples below. Examples: plot ... using 1:2:3:4 with vectors filled heads plot ... using 1:2:3:4 with vectors arrowstyle 3 plot ... using 1:2:3:4:5 with vectors arrowstyle variable splot 'file.dat' using 1:2:3:(1):(1):(1) with vectors filled head lw 2 Notes: You cannot mix the `arrowstyle` keyword with other line style qualifiers in the plot command. An additional column of color values is required if the arrow style includes `lc variable` or `lc rgb variable`. splot with vectors is supported only for `set mapping cartesian`. `set clip one` and `set clip two` affect vectors drawn in 2D. See `set clip` and `arrowstyle`. See also the 2D plot style `with arrows` that is identical to `with vectors` except that each arrow is specified using x:y:length:angle. #TeX \newpage 2 xerrorbars ?plotting styles xerrorbars ?style xerrorbars ?with xerrorbars ?xerrorbars Ffigure_xerrorbars The `xerrorbars` style is only relevant to 2D data plots. `xerrorbars` is like `points`, except that a horizontal error bar is also drawn. At each point (x,y), a line is drawn from (xlow,y) to (xhigh,y) or from (x-xdelta,y) to (x+xdelta,y), depending on how many data columns are provided. The appearance of the tic mark at the ends of the bar is controlled by `set errorbars`. The clearance between the point and the error bars is controlled by `set pointintervalbox`. The basic style requires either 3 or 4 columns: 3 columns: x y xdelta 4 columns: x y xlow xhigh An additional input column (4th or 5th) may be used to provide variable color. This style does not permit variable point properties. 2 xyerrorbars ?plotting styles xyerrorbars ?style xyerrorbars ?with xyerrorbars ?xyerrorbars Ffigure_xyerrorbars The `xyerrorbars` style is only relevant to 2D data plots. `xyerrorbars` is like `points`, except that horizontal and vertical error bars are also drawn. At each point (x,y), lines are drawn from (x,y-ydelta) to (x,y+ydelta) and from (x-xdelta,y) to (x+xdelta,y) or from (x,ylow) to (x,yhigh) and from (xlow,y) to (xhigh,y), depending upon the number of data columns provided. The appearance of the tic mark at the ends of the bar is controlled by `set errorbars`. The clearance between the point and the error bars is controlled by `set pointintervalbox`. Either 4 or 6 input columns are required. 4 columns: x y xdelta ydelta 6 columns: x y xlow xhigh ylow yhigh If data are provided in an unsupported mixed form, the `using` specifier of the `plot` command should be used to set up the appropriate form. For example, if the data are of the form (x,y,xdelta,ylow,yhigh), then you can use plot 'data' using 1:2:($1-$3):($1+$3):4:5 with xyerrorbars An additional input column (5th or 7th) may be used to provide variable color. This style does not permit variable point properties. #TeX \newpage 2 xerrorlines ?plotting styles xerrorlines ?style xerrorlines ?with xerrorlines ?xerrorlines Ffigure_xerrorlines The `xerrorlines` style is only relevant to 2D data plots. `xerrorlines` is like `linespoints`, except that a horizontal error line is also drawn. At each point (x,y), a line is drawn from (xlow,y) to (xhigh,y) or from (x-xdelta,y) to (x+xdelta,y), depending on how many data columns are provided. The appearance of the tic mark at the ends of the bar is controlled by `set errorbars`. The basic style requires either 3 or 4 columns: 3 columns: x y xdelta 4 columns: x y xlow xhigh An additional input column (4th or 5th) may be used to provide variable color. This style does not permit variable point properties. 2 xyerrorlines ?plotting styles xyerrorlines ?style xyerrorlines ?with xyerrorlines ?xyerrorlines Ffigure_xyerrorlines The `xyerrorlines` style is only relevant to 2D data plots. `xyerrorlines` is like `linespoints`, except that horizontal and vertical error bars are also drawn. At each point (x,y), lines are drawn from (x,y-ydelta) to (x,y+ydelta) and from (x-xdelta,y) to (x+xdelta,y) or from (x,ylow) to (x,yhigh) and from (xlow,y) to (xhigh,y), depending upon the number of data columns provided. The appearance of the tic mark at the ends of the bar is controlled by `set errorbars`. Either 4 or 6 input columns are required. 4 columns: x y xdelta ydelta 6 columns: x y xlow xhigh ylow yhigh If data are provided in an unsupported mixed form, the `using` specifier of the `plot` command should be used to set up the appropriate form. For example, if the data are of the form (x,y,xdelta,ylow,yhigh), then you can use plot 'data' using 1:2:($1-$3):($1+$3):4:5 with xyerrorlines An additional input column (5th or 7th) may be used to provide variable color. This style does not permit variable point properties. 2 yerrorbars ?plotting styles yerrorbars ?plotting styles errorbars ?style yerrorbars ?with yerrorbars ?style errorbars ?with errorbars ?yerrorbars =errorbars Ffigure_yerrorbars The `yerrorbars` (or `errorbars`) style is only relevant to 2D data plots. `yerrorbars` is like `points`, except that a vertical error bar is also drawn. At each point (x,y), a line is drawn from (x,y-ydelta) to (x,y+ydelta) or from (x,ylow) to (x,yhigh), depending on how many data columns are provided. The appearance of the tic mark at the ends of the bar is controlled by `set errorbars`. The clearance between the point and the error bars is controlled by `set pointintervalbox`. 2 columns: [implicit x] y ydelta 3 columns: x y ydelta 4 columns: x y ylow yhigh Additional input columns may be used to provide information such as variable point size, point type, or color. See also ^ <a href="https://www.apklas.com?arsae=http%3A%2F%2Fwww.gnuplot.info%2Fdemo%2Fmgr.html" target="_parent"> errorbar demo. ^ </a> 2 yerrorlines ?plotting styles yerrorlines ?plotting styles errorlines ?style yerrorlines ?with yerrorlines ?style errorlines ?with errorlines ?yerrorlines ?errorlines Ffigure_yerrorlines The `yerrorlines` (or `errorlines`) style is only relevant to 2D data plots. `yerrorlines` is like `linespoints`, except that a vertical error line is also drawn. At each point (x,y), a line is drawn from (x,y-ydelta) to (x,y+ydelta) or from (x,ylow) to (x,yhigh), depending on how many data columns are provided. The appearance of the tic mark at the ends of the bar is controlled by `set errorbars`. Either 3 or 4 input columns are required. 3 columns: x y ydelta 4 columns: x y ylow yhigh Additional input columns may be used to provide information such as variable point size, point type, or color. See also ^ <a href="https://www.apklas.com?arsae=http%3A%2F%2Fwww.gnuplot.info%2Fdemo%2Fmgr.html" target="_parent"> errorbar demo. ^ </a> #TeX \newpage 2 3D plots ?3D plots ?plotting styles 3D plots =3D 3D plots are generated using the command `splot` rather than `plot`. Many of the 2D plot styles (points, images, impulse, labels, vectors) can also be used in 3D by providing an extra column of data containing z coordinate. Some plot types (pm3d coloring, surfaces, contours) must be generated using the `splot` command even if only a 2D projection is wanted. 3 surface plots ?surface plots =surface Ffigure_surface+contours The styles `splot with lines` and `splot with surface` both generate a surface made from a grid of lines. Solid surfaces can be generated using the style `splot with pm3d`. Usually the surface is displayed at some convenient viewing angle, such that it clearly represents a 3D surface. See `set view`. In this case the X, Y, and Z axes are all visible in the plot. The illusion of 3D is enhanced by choosing hidden line removal. See `hidden3d`. The `splot` command can also calculate and draw contour lines corresponding to constant Z values. These contour lines may be drawn onto the surface itself, or projected onto the XY plane. See `set contour`. 3 2D projection (set view map) ?2D projection (set view map) Ffigure_mapcontours An important special case of the `splot` command is to map the Z coordinate onto a 2D surface by projecting the plot along the Z axis onto the xy plane. See `set view map`. This plot mode is useful for contour plots and heat maps. This figure shows contours plotted once with plot style `lines` and once with style `labels`. 3 PM3D plots ?PM3D PLOTS Ffigure_pm3dsolid 3D surfaces can also be drawn using solid pm3d quadrangles rather than lines. In this case there is no hidden surface removal, but if the component facets are drawn back-to-front then a similar effect is achieved. See `set pm3d depthorder`. While pm3d surfaces are by default colored using a smooth color palette (see `set palette`), it is also possible to specify a solid color surface or to specify distinct solid colors for the top and bottom surfaces as in the figure shown here. See `pm3d fillcolor`. Unlike the line-trimming in hidden3d mode, pm3d surfaces can be smoothly clipped to the current zrange. See `set pm3d clipping`. #TeX \newpage 2 Fence plots ?fenceplots =zerrorfill Ffigure_fenceplot Fence plots combine several 2D plots by aligning their Y coordinates and separating them from each other by a displacement along X. Filling the area between a base value and each plot's series of Z values enhances the visual impact of the alignment on Y and comparison on Z. There are several ways such plots can be created in gnuplot. The simplest is to use the 5 column variant of the `zerrorfill` style. Suppose there are separate curves z = Fi(y) indexed by i. A fence plot is generated by `splot with zerrorfill` using input columns i y z_base z_base Fi(y) 2 isosurface ?plotting styles isosurface ?style isosurface ?with isosurface ?isosurface Ffigure_isosurface This 3D plot style requires a populated voxel grid (see `set vgrid`, `vfill`). Linear interpolation of voxel grid values is used to estimate fractional grid coordinates corresponding to the requested isolevel. These points are then used to generate a tessellated surface. The facets making up the surface are rendered as pm3d polygons, so the surface coloring, transparency, and border properties are controlled by `set pm3d`. In general the surface is easier to interpret visually if facets are given a thin border that is darker than the fill color. By default the tessellation uses a mixture of quadrangles and triangles. To use triangle only, see `set isosurface`. Example: set style fill solid 0.3 set pm3d depthorder border lc "blue" lw 0.2 splot $helix with isosurface level 10 fc "cyan" 2 Zerrorfill ?plotting styles zerrorfill ?style zerrorfill ?with zerrorfill ?zerrorfill Syntax: splot DATA using 1:2:3:4[:5] with zerrorfill {fc|fillcolor <colorspec>} {lt|linetype <n>} {<line properties>} The `zerrorfill` plot style is similar to one variant of the 2D plot style `filledcurves`. It fills the area between two functions or data lines that are sampled at the same x and y points. It requires 4 or 5 input columns: 4 columns: x y z zdelta 5 columns: x y z zlow zhigh Ffigure_zerror The area between zlow and zhigh is filled and then a line is drawn through the z values. By default both the line and the fill area use the same color, but you can change this in the splot command. The fill area properties are also affected by the global fill style; see `set style fill`. If there are multiple curves in the splot command each new curve may occlude all previous curves. To get proper depth sorting so that curves can only be occluded by curves closer to the viewer, use `set pm3d depthorder base`. Unfortunately this causes all the filled areas to be drawn after all of the corresponding lines of z values. In order to see both the lines and the depth-sorted fill areas you probably will need to make the fill areas partially transparent or use pattern fill rather than solid fill. The fill area in the first two examples below is the same. splot 'data' using 1:2:3:4 with zerrorfill fillcolor "grey" lt black splot 'data' using 1:2:3:($3-$4):($3+$4) with zerrorfill splot '+' using 1:(const):(func1($1)):(func2($1)) with zerrorfill splot for [k=1:5] datafile[k] with zerrorfill lt black fc lt (k+1) This plot style can also be used to create fence plots. See `fenceplots`. 2 Animation ?animation Any of gnuplot's interactive terminals (qt win wxt x11 aqua) can be used to display an animation by plotting successive frames from the command line or from a script. Several non-mousing terminals also support some form of animation. See `term sixelgd`, `term kittycairo`. Two terminals can save an animation to a file for later playback locally or by embedding it a web page. See `term gif animate`, `term webp`. ^ <p align="center"> ^ <picture> ^ <source srcset="figure_spinning_d20.webp" type="image/webp"> ^ <img src="figure_static_d20.png"> ^ </source></picture> Example: unset border; unset tics; unset key; set view equal xyz set pm3d border linecolor "black" set term webp animate delay 50 set output 'spinning_d20.webp' do for [ang=1:360:2] { set view 60, ang splot 'icosahedron.dat' with polygons fc "gold" } unset output 1 Commands ?commands This section lists the commands acceptable to `gnuplot` in alphabetical order. Printed versions of this document contain all commands; the text available interactively may not be complete. Indeed, on some systems there may be no commands at all listed under this heading. Note that in most cases unambiguous abbreviations for command names and their options are permissible, i.e., "`p f(x) w li`" instead of "`plot f(x) with lines`". In the syntax descriptions, braces ({}) denote optional arguments and a vertical bar (|) separates mutually exclusive choices. 2 Break ?commands break ?break The `break` command is only meaningful inside the bracketed iteration clause of a `do` or `while` statement. It causes the remaining statements inside the bracketed clause to be skipped and iteration is terminated. Execution resumes at the statement following the closing bracket. See also `continue`. 2 cd ?commands cd ?cd The `cd` command changes the working directory. Syntax: cd '<directory-name>' The directory name must be enclosed in quotes. Examples: cd 'subdir' cd ".." It is recommended that Windows users use single-quotes, because backslash [\] has special significance inside double-quotes and has to be escaped. For example, cd "c:\newdata" fails, but cd 'c:\newdata' cd "c:\\newdata" work as expected. 2 call ?commands call ?call The `call` command is identical to the `load` command with one exception: the name of the file being loaded may be followed by up to nine parameters. call "inputfile" <param-1> <param-2> <param-3> ... <param-9> Gnuplot now provides a set of string variables ARG0, ARG1, ..., ARG9 and an integer variable ARGC. When a `call` command is executed ARG0 is set to the name of the input file, ARGC is set to the number of parameters present, and ARG1 to ARG9 are loaded from the parameters that follow it on the command line. Any existing contents of the ARG variables are saved and restored across a `call` command. Because the parameters ARG1 ... ARG9 are stored in ordinary string variables they may be dereferenced by macro expansion. However in many cases it is more natural to use them as you would any other variable. In parallel with the string representation of parameters ARG1 ... ARG9, the parameters themselves are stored in an array ARGV[9]. See `ARGV`. DEPRECATED: Versions prior to 5.0 performed macro-like substitution of the special tokens $0, $1, ... $9 with the literal contents of <param-1> ... That older mechanism is no longer supported. EXPERIMENTAL: Function blocks (new in this version) provide a more flexible alternative to `call`. See `function blocks`. 3 ARGV[ ] ?argv ?ARGV ?call argv ?call ARGV When a gnuplot script is entered via the `call` command any parameters passed by the caller are available via two mechanisms. Each parameter is stored as a string in variables ARG1, ARG2, ... ARG9. Each parameter is also stored as one element of the array ARGV[9]. Numerical values are stored as complex variables. All other values are stored as strings. ARGC holds the number of parameters. Thus after a call call 'routine_1.gp' 1 pi "title" The three arguments are available inside routine_1.gp as follows ARGC = 3 ARG1 = "1" ARGV[1] = 1.0 ARG2 = "3.14159" ARGV[2] = 3.14159265358979... ARG3 = "title" ARGV[3] = "title" In this example ARGV[1] and ARGV[2] have the full precision of a floating point variable. ARG2 lost precision in being stored as a string using format "%g". 3 Example ?call example ?commands call example Call site MYFILE = "script1.gp" FUNC = "sin(x)" call MYFILE FUNC 1.23 "This is a plot title" Upon entry to the called script ARG0 holds "script1.gp" ARG1 holds the string "sin(x)" ARG2 holds the string "1.23" ARG3 holds the string "This is a plot title" ARGC is 3 The script itself can now execute plot @ARG1 with lines title ARG3 print ARG2 * 4.56, @ARG2 * 4.56 print "This plot produced by script ", ARG0 Notice that because ARG1 is a string it must be dereferenced as a macro, but ARG2 may be dereferenced either as a macro (yielding a numerical constant) or a variable (yielding that same numerical value after auto-promotion of the string "1.23" to a real). The same result could be obtained directly from a shell script by invoking gnuplot with the `-c` command line option: gnuplot -persist -c "script1.gp" "sin(x)" 1.23 "This is a plot title" 2 clear ?commands clear ?clear =inset ?inset The `clear` command erases the current screen or output device as specified by `set terminal` and `set output`. This usually generates a formfeed on hardcopy devices. For some terminals `clear` erases only the portion of the plotting surface defined by `set size`, so for these it can be used in conjunction with `set multiplot` to create an inset. Example: set multiplot plot sin(x) set origin 0.5,0.5 set size 0.4,0.4 clear plot cos(x) unset multiplot Please see `set multiplot`, `set size`, and `set origin` for details. 2 Continue ?commands continue ?continue The `continue` command is only meaningful inside the bracketed iteration clause of a `do` or `while` statement. It causes the remaining statements inside the bracketed clause to be skipped. Execution resumes at the start of the next iteration (if any remain in the loop condition). See also `break`. 2 Do ?commands do ?do Syntax: do for <iteration-spec> { <commands> <commands> } Execute a sequence of commands multiple times. The commands must be enclosed in curly brackets, and the opening "{" must be on the same line as the `do` keyword. This command cannot be used with old-style (un-bracketed) if/else statements. See `if`. For examples of iteration specifiers, see `iteration`. Example: set multiplot layout 2,2 do for [name in "A B C D"] { filename = name . ".dat" set title sprintf("Condition %s",name) plot filename title name } unset multiplot See also `while`, `continue`, `break`. 2 evaluate ?commands evaluate ?evaluate The `evaluate` command executes gnuplot commands contained in a string or in a function block. Newline characters are not allowed within the string. evaluate "commands in a string constant" evaluate string_valued_function( ... arguments ... ) evaluate $functionblock( ... arguments ... ) This is especially useful for a repetition of similar commands. Example: set_label(x, y, text) \ = sprintf("set label '%s' at %f, %f point pt 5", text, x, y) eval set_label(1., 1., 'one/one') eval set_label(2., 1., 'two/one') eval set_label(1., 2., 'one/two') Please see `function blocks` and `substitution macros` for other mechanisms that construct or execute strings containing gnuplot commands. 2 exit ?commands exit ?exit exit exit message "error message text" exit status <integer error code> The commands `exit` and `quit`, as well as the END-OF-FILE character (usually Ctrl-D) terminate input from the current input stream: terminal session, pipe, or file input (pipe). If input streams are nested (inherited `load` scripts), then reading will continue in the parent stream. When the top level stream is closed, the program itself will exit. The command `exit gnuplot` will immediately and unconditionally cause gnuplot to exit even if the input stream is multiply nested. In this case any open output files may not be completed cleanly. Example of use: bind "ctrl-x" "unset output; exit gnuplot" The command `exit error "error message"` simulates a program error. In interactive mode it prints the error message and returns to the command line, breaking out of all nested loops or calls. In non-interactive mode the program will exit. When gnuplot exits to the controlling shell, the return value is not usually informative. This variant of the command allows you to return a specific value. exit status <value> See help for `batch/interactive` for more details. 2 fit ?commands fit ?fit ?least-squares ?Marquardt The `fit` command fits a user-supplied real-valued expression to a set of data points, using the nonlinear least-squares Marquardt-Levenberg algorithm. There can be up to 12 independent variables, there is always 1 dependent variable, and any number of parameters can be fitted. Optionally, error estimates can be input for weighting the data points. The basic use of `fit` is best explained by a simple example where a set of measured x and y values read from a file are used to be modeled by a function y = f(x). f(x) = a + b*x + c*x**2 fit f(x) 'measured.dat' using 1:2 via a,b,c plot 'measured.dat' u 1:2, f(x) Syntax: fit {<ranges>} <expression> '<datafile>' {datafile-modifiers} {{unitweights} | {y|xy|z}error | errors <var1>{,<var2>,...}} via '<parameter file>' | <var1>{,<var2>,...} Ranges may be specified to filter the data used in fitting. Out-of-range data points are ignored. The syntax is [{dummy_variable=}{<min>}{:<max>}], analogous to `plot`; see `plot ranges`. <expression> can be any valid `gnuplot` expression, although the most common is a previously user-defined function of the form f(x) or f(x,y). It must be real-valued. The names of the independent variables are set by the `set dummy` command, or in the <ranges> part of the command (see below); by default, the first two are called x and y. Furthermore, the expression should depend on one or more variables whose value is to be determined by the fitting procedure. <datafile> is treated as in the `plot` command. All the `plot datafile` modifiers (`using`, `every`,...) except `smooth` are applicable to `fit`. See `plot datafile`. The datafile contents can be interpreted flexibly by providing a `using` qualifier as with plot commands. For example to generate the independent variable x as the sum of columns 2 and 3, while taking z from column 6 and requesting equal weights: fit ... using ($2+$3):6 In the absence of a `using` specification, the fit implicitly assumes there is only a single independent variable. If the file itself, or the using specification, contains only a single column of data, the line number is taken as the independent variable. If a `using` specification is given, there can be up to 12 independent variables (and more if specially configured at compile time). The `unitweights` option, which is the default, causes all data points to be weighted equally. This can be changed by using the `errors` keyword to read error estimates of one or more of the variables from the data file. These error estimates are interpreted as the standard deviation s of the corresponding variable value and used to compute a weight for the datum as 1/s**2. In case of error estimates of the independent variables, these weights are further multiplied by fitting function derivatives according to the "effective variance method" (Jay Orear, Am. J. Phys., Vol. 50, 1982). The `errors` keyword is to be followed by a comma-separated list of one or more variable names for which errors are to be input; the dependent variable z must always be among them, while independent variables are optional. For each variable in this list, an additional column will be read from the file, containing that variable's error estimate. Again, flexible interpretation is possible by providing the `using` qualifier. Note that the number of independent variables is thus implicitly given by the total number of columns in the `using` qualifier, minus 1 (for the dependent variable), minus the number of variables in the `errors` qualifier. As an example, if one has 2 independent variables, and errors for the first independent variable and the dependent variable, one uses the `errors x,z` qualifier, and a `using` qualifier with 5 columns, which are interpreted as x:y:z:sx:sz (where x and y are the independent variables, z the dependent variable, and sx and sz the standard deviations of x and z). A few shorthands for the `errors` qualifier are available: `yerrors` (for fits with 1 column of independent variable), and `zerrors` (for the general case) are all equivalent to `errors z`, indicating that there is a single extra column with errors of the dependent variable. `xyerrors`, for the case of 1 independent variable, indicates that there are two extra columns, with errors of both the independent and the dependent variable. In this case the errors on x and y are treated by Orear's effective variance method. Note that `yerror` and `xyerror` are similar in both form and interpretation to the `yerrorlines` and `xyerrorlines` 2D plot styles. With the command `set fit v4` the fit command syntax is compatible with `gnuplot` version 4. In this case there must be two more `using` qualifiers (z and s) than there are independent variables, unless there is only one variable. `gnuplot` then uses the following formats, depending on the number of columns given in the `using` specification: z # 1 independent variable (line number) x:z # 1 independent variable (1st column) x:z:s # 1 independent variable (3 columns total) x:y:z:s # 2 independent variables (4 columns total) x1:x2:x3:z:s # 3 independent variables (5 columns total) x1:x2:x3:...:xN:z:s # N independent variables (N+2 columns total) Please beware that this means that you have to supply z-errors s in a fit with two or more independent variables. If you want unit weights you need to supply them explicitly by using e.g. then format x:y:z:(1). The dummy variable names may be changed when specifying a range as noted above. The first range corresponds to the first `using` spec, and so on. A range may also be given for z (the dependent variable), in which case data points for which f(x,...) is out of the z range will not contribute to the residual being minimized. Multiple datasets may be simultaneously fit with functions of one independent variable by making y a 'pseudo-variable', e.g., the dataline number, and fitting as two independent variables. See `fit multi-branch`. The `via` qualifier specifies which parameters are to be optimized, either directly, or by referencing a parameter file. Examples: f(x) = a*x**2 + b*x + c g(x,y) = a*x**2 + b*y**2 + c*x*y set fit limit 1e-6 fit f(x) 'measured.dat' via 'start.par' fit f(x) 'measured.dat' using 3:($7-5) via 'start.par' fit f(x) './data/trash.dat' using 1:2:3 yerror via a, b, c fit g(x,y) 'surface.dat' using 1:2:3 via a, b, c fit a0 + a1*x/(1 + a2*x/(1 + a3*x)) 'measured.dat' via a0,a1,a2,a3 fit a*x + b*y 'surface.dat' using 1:2:3 via a,b fit [*:*][yaks=*:*] a*x+b*yaks 'surface.dat' u 1:2:3 via a,b fit [][][t=*:*] a*x + b*y + c*t 'foo.dat' using 1:2:3:4 via a,b,c set dummy x1, x2, x3, x4, x5 h(x1,x2,x3,x4,s5) = a*x1 + b*x2 + c*x3 + d*x4 + e*x5 fit h(x1,x2,x3,x4,x5) 'foo.dat' using 1:2:3:4:5:6 via a,b,c,d,e After each iteration step, detailed information about the current state of the fit is written to the display. The same information about the initial and final states is written to a log file, "fit.log". This file is always appended to, so as to not lose any previous fit history; it should be deleted or renamed as desired. By using the command `set fit logfile`, the name of the log file can be changed. If activated by using `set fit errorvariables`, the error for each fitted parameter will be stored in a variable named like the parameter, but with "_err" appended. Thus the errors can be used as input for further computations. If `set fit prescale` is activated, fit parameters are prescaled by their initial values. This helps the Marquardt-Levenberg routine converge more quickly and reliably in cases where parameters differ in size by several orders of magnitude. The fit may be interrupted by pressing Ctrl-C (Ctrl-Break in wgnuplot). After the current iteration completes, you have the option to (1) stop the fit and accept the current parameter values, (2) continue the fit, (3) execute a `gnuplot` command as specified by `set fit script` or the environment variable `FIT_SCRIPT`. The default is `replot`, so if you had previously plotted both the data and the fitting function in one graph, you can display the current state of the fit. Once `fit` has finished, the `save fit` command may be used to store final values in a file for subsequent use as a parameter file. See `save fit` for details. 3 adjustable parameters ?commands fit parameters ?fit parameters ?commands fit adjustable_parameters ?fit adjustable_parameters ?fit_parameters There are two ways that `via` can specify the parameters to be adjusted, either directly on the command line or indirectly, by referencing a parameter file. The two use different means to set initial values. Adjustable parameters can be specified by a comma-separated list of variable names after the `via` keyword. Any variable that is not already defined is created with an initial value of 1.0. However, the fit is more likely to converge rapidly if the variables have been previously declared with more appropriate starting values. In a parameter file, each parameter to be varied and a corresponding initial value are specified, one per line, in the form varname = value Comments, marked by '#', and blank lines are permissible. The special form varname = value # FIXED means that the variable is treated as a 'fixed parameter', initialized by the parameter file, but not adjusted by `fit`. For clarity, it may be useful to designate variables as fixed parameters so that their values are reported by `fit`. The keyword `# FIXED` has to appear in exactly this form. 3 short introduction ?commands fit beginners_guide ?fit beginners_guide ?fit guide ?fitting `fit` is used to find a set of parameters that 'best' fits your data to your user-defined function. The fit is judged on the basis of the sum of the squared differences or 'residuals' (SSR) between the input data points and the function values, evaluated at the same places. This quantity is often called 'chisquare' (i.e., the Greek letter chi, to the power of 2). The algorithm attempts to minimize SSR, or more precisely the weighted sum of squared residuals (WSSR), for which the residuals are weighted by the input data errors before being squared; see `fit error_estimates` for details. That's why it is called 'least-squares fitting'. Let's look at an example to see what is meant by 'non-linear', but first we had better go over some terms. Here it is convenient to use z as the dependent variable for user-defined functions of either one independent variable, z=f(x), or two independent variables, z=f(x,y). A parameter is a user-defined variable that `fit` will adjust, i.e., an unknown quantity in the function declaration. Linearity/non-linearity refers to the relationship of the dependent variable, z, to the parameters which `fit` is adjusting, not of z to the independent variables, x and/or y. (To be technical, the second {and higher} derivatives of the fitting function with respect to the parameters are zero for a linear least-squares problem). For linear least-squares the user-defined function will be a sum of simple functions, not involving any parameters, each multiplied by one parameter. Nonlinear least-squares handles more complicated functions in which parameters can be used in a large number of ways. An example that illustrates the difference between linear and nonlinear least-squares is the Fourier series. One member may be written as z=a*sin(c*x) + b*cos(c*x). If a and b are the unknown parameters and c is constant, then estimating values of the parameters is a linear least-squares problem. However, if c is an unknown parameter, the problem is nonlinear. In the linear case, parameter values can be determined by comparatively simple linear algebra, in one direct step. However the linear special case is also solved along with more general nonlinear problems by the iterative procedure that `gnuplot` uses. `fit` attempts to find the minimum by doing a search. Each step (iteration) calculates WSSR with a new set of parameter values. The Marquardt-Levenberg algorithm selects the parameter values for the next iteration. The process continues until a preset criterion is met, either (1) the fit has "converged" (the relative change in WSSR is less than a certain limit, see `set fit limit`), or (2) it reaches a preset iteration count limit (see `set fit maxiter`). The fit may also be interrupted and subsequently halted from the keyboard (see `fit`). The user variable FIT_CONVERGED contains 1 if the previous fit command terminated due to convergence; it contains 0 if the previous fit terminated for any other reason. FIT_NITER contains the number of iterations that were done during the last fit. Often the function to be fitted will be based on a model (or theory) that attempts to describe or predict the behaviour of the data. Then `fit` can be used to find values for the free parameters of the model, to determine how well the data fits the model, and to estimate an error range for each parameter. See `fit error_estimates`. Alternatively, in curve-fitting, functions are selected independent of a model (on the basis of experience as to which are likely to describe the trend of the data with the desired resolution and a minimum number of parameters*functions.) The `fit` solution then provides an analytic representation of the curve. However, if all you really want is a smooth curve through your data points, the `smooth` option to `plot` may be what you've been looking for rather than `fit`. 3 error estimates ?commands fit error_estimates ?fit error_estimates ?fit errors In `fit`, the term "error" is used in two different contexts, data error estimates and parameter error estimates. Data error estimates are used to calculate the relative weight of each data point when determining the weighted sum of squared residuals, WSSR or chisquare. They can affect the parameter estimates, since they determine how much influence the deviation of each data point from the fitted function has on the final values. Some of the `fit` output information, including the parameter error estimates, is more meaningful if accurate data error estimates have been provided. The `statistical overview` describes some of the `fit` output and gives some background for the 'practical guidelines'. 4 statistical overview ?commands fit error statistical_overview ?statistical_overview The theory of non-linear least-squares is generally described in terms of a normal distribution of errors, that is, the input data is assumed to be a sample from a population having a given mean and a Gaussian (normal) distribution about the mean with a given standard deviation. For a sample of sufficiently large size, and knowing the population standard deviation, one can use the statistics of the chisquare distribution to describe a "goodness of fit" by looking at the variable often called "chisquare". Here, it is sufficient to say that a reduced chisquare (chisquare/degrees of freedom, where degrees of freedom is the number of datapoints less the number of parameters being fitted) of 1.0 is an indication that the weighted sum of squared deviations between the fitted function and the data points is the same as that expected for a random sample from a population characterized by the function with the current value of the parameters and the given standard deviations. If the standard deviation for the population is not constant, as in counting statistics where variance = counts, then each point should be individually weighted when comparing the observed sum of deviations and the expected sum of deviations. At the conclusion `fit` reports 'stdfit', the standard deviation of the fit, which is the rms of the residuals, and the variance of the residuals, also called 'reduced chisquare' when the data points are weighted. The number of degrees of freedom (the number of data points minus the number of fitted parameters) is used in these estimates because the parameters used in calculating the residuals of the datapoints were obtained from the same data. If the data points have weights, `gnuplot` calculates the so-called p-value, i.e. one minus the cumulative distribution function of the chisquare-distribution for the number of degrees of freedom and the resulting chisquare, see `fit practical_guidelines`. These values are exported to the variables FIT_NDF = Number of degrees of freedom FIT_WSSR = Weighted sum-of-squares residual FIT_STDFIT = sqrt(WSSR/NDF) FIT_P = p-value To estimate confidence levels for the parameters, one can use the minimum chisquare obtained from the fit and chisquare statistics to determine the value of chisquare corresponding to the desired confidence level, but considerably more calculation is required to determine the combinations of parameters which produce such values. Rather than determine confidence intervals, `fit` reports parameter error estimates which are readily obtained from the variance-covariance matrix after the final iteration. By convention, these estimates are called "standard errors" or "asymptotic standard errors", since they are calculated in the same way as the standard errors (standard deviation of each parameter) of a linear least-squares problem, even though the statistical conditions for designating the quantity calculated to be a standard deviation are not generally valid for a nonlinear least-squares problem. The asymptotic standard errors are generally over-optimistic and should not be used for determining confidence levels, but are useful for qualitative purposes. The final solution also produces a correlation matrix indicating correlation of parameters in the region of the solution; The main diagonal elements, autocorrelation, are always 1; if all parameters were independent, the off-diagonal elements would be nearly 0. Two variables which completely compensate each other would have an off-diagonal element of unit magnitude, with a sign depending on whether the relation is proportional or inversely proportional. The smaller the magnitudes of the off-diagonal elements, the closer the estimates of the standard deviation of each parameter would be to the asymptotic standard error. 4 practical guidelines ?commands fit error practical_guidelines ?fit practical_guidelines ?fit guidelines If you have a basis for assigning weights to each data point, doing so lets you make use of additional knowledge about your measurements, e.g., take into account that some points may be more reliable than others. That may affect the final values of the parameters. Weighting the data provides a basis for interpreting the additional `fit` output after the last iteration. Even if you weight each point equally, estimating an average standard deviation rather than using a weight of 1 makes WSSR a dimensionless variable, as chisquare is by definition. Each fit iteration will display information which can be used to evaluate the progress of the fit. (An '*' indicates that it did not find a smaller WSSR and is trying again.) The 'sum of squares of residuals', also called 'chisquare', is the WSSR between the data and your fitted function; `fit` has minimized that. At this stage, with weighted data, chisquare is expected to approach the number of degrees of freedom (data points minus parameters). The WSSR can be used to calculate the reduced chisquare (WSSR/ndf) or stdfit, the standard deviation of the fit, sqrt(WSSR/ndf). Both of these are reported for the final WSSR. If the data are unweighted, stdfit is the rms value of the deviation of the data from the fitted function, in user units. If you supplied valid data errors, the number of data points is large enough, and the model is correct, the reduced chisquare should be about unity. (For details, look up the 'chi-squared distribution' in your favorite statistics reference.) If so, there are additional tests, beyond the scope of this overview, for determining how well the model fits the data. A reduced chisquare much larger than 1.0 may be due to incorrect data error estimates, data errors not normally distributed, systematic measurement errors, 'outliers', or an incorrect model function. A plot of the residuals, e.g., `plot 'datafile' using 1:($2-f($1))`, may help to show any systematic trends. Plotting both the data points and the function may help to suggest another model. Similarly, a reduced chisquare less than 1.0 indicates WSSR is less than that expected for a random sample from the function with normally distributed errors. The data error estimates may be too large, the statistical assumptions may not be justified, or the model function may be too general, fitting fluctuations in a particular sample in addition to the underlying trends. In the latter case, a simpler function may be more appropriate. The p-value of the fit is one minus the cumulative distribution function of the chisquare-distribution for the number of degrees of freedom and the resulting chisquare. This can serve as a measure of the goodness-of-fit. The range of the p-value is between zero and one. A very small or large p-value indicates that the model does not describe the data and its errors well. As described above, this might indicate a problem with the data, its errors or the model, or a combination thereof. A small p-value might indicate that the errors have been underestimated and the errors of the final parameters should thus be scaled. See also `set fit errorscaling`. You'll have to get used to both `fit` and the kind of problems you apply it to before you can relate the standard errors to some more practical estimates of parameter uncertainties or evaluate the significance of the correlation matrix. Note that `fit`, in common with most nonlinear least-squares implementations, minimizes the weighted sum of squared distances (y-f(x))**2. It does not provide any means to account for "errors" in the values of x, only in y. Also, any "outliers" (data points outside the normal distribution of the model) will have an exaggerated effect on the solution. 3 control ?commands fit control ?fit control =FIT_LOG =FIT_SCRIPT There are two environment variables that can be defined to affect `fit`. The environment variables must be defined before `gnuplot` is executed; how to do so depends on your operating system. FIT_LOG changes the name (and/or path) of the file to which the fit log will be written. The default is to write "fit.log" in the current working directory. This can be overwritten at run time using the command `set fit logfile`. FIT_SCRIPT specifies a command that may be executed after an user interrupt. The default is `replot`, but a `plot` or `load` command may be useful to display a plot customized to highlight the progress of the fit. This can be changed at run time using `set fit script`. For many other run time adjustments to way fit works, see `set fit`. 3 error recovery ?commands fit error_recovery ?fit error_recovery Starting with gnuplot version 6, the `fit` command always returns to the next command input line regardless of the success or failure of fitting. This allows scripted recovery from fit errors. The variable FIT_ERROR is set to 0 on success, non-zero on error. This example plots however many of five data sets can be successfully fit. Failure for data set 2 would not prevent fitting data sets 3 through 5. do for [i=1:5] { DATA = sprintf("Data_%05d.dat", i) fit f(x) DATA via a,b,c if (FIT_ERROR || !FIT_CONVERGED) { print "Fit failed for ", DATA continue } set output sprintf("dataset_%05.png", i) plot DATA, f(x) unset output } 3 multi-branch ?commands fit multi-branch ?fit multi-branch ?multi-branch ?branch In multi-branch fitting, multiple data sets can be simultaneously fit with functions of one independent variable having common parameters by minimizing the total WSSR. The function and parameters (branch) for each data set are selected by using a 'pseudo-variable', e.g., either the dataline number (a 'column' index of -1) or the datafile index (-2), as the second independent variable. Example: Given two exponential decays of the form, z=f(x), each describing a different data set but having a common decay time, estimate the values of the parameters. If the datafile has the format x:z:s, then f(x,y) = (y==0) ? a*exp(-x/tau) : b*exp(-x/tau) fit f(x,y) 'datafile' using 1:-2:2:3 via a, b, tau For a more complicated example, see the file "hexa.fnc" used by the "fit.dem" demo. Appropriate weighting may be required since unit weights may cause one branch to predominate if there is a difference in the scale of the dependent variable. Fitting each branch separately, using the multi-branch solution as initial values, may give an indication as to the relative effect of each branch on the joint solution. 3 starting values ?commands fit starting_values ?fit starting_values ?starting_values Nonlinear fitting is not guaranteed to converge to the global optimum (the solution with the smallest sum of squared residuals, SSR), and can get stuck at a local minimum. The routine has no way to determine that; it is up to you to judge whether this has happened. `fit` may, and often will get "lost" if started far from a solution, where SSR is large and changing slowly as the parameters are varied, or it may reach a numerically unstable region (e.g., too large a number causing a floating point overflow) which results in an "undefined value" message or `gnuplot` halting. To improve the chances of finding the global optimum, you should set the starting values at least roughly in the vicinity of the solution, e.g., within an order of magnitude, if possible. The closer your starting values are to the solution, the less chance of stopping at a false minimum. One way to find starting values is to plot data and the fitting function on the same graph and change parameter values and `replot` until reasonable similarity is reached. The same plot is also useful to check whether the fit found a false minimum. Of course finding a nice-looking fit does not prove there is no "better" fit (in either a statistical sense, characterized by an improved goodness-of-fit criterion, or a physical sense, with a solution more consistent with the model.) Depending on the problem, it may be desirable to `fit` with various sets of starting values, covering a reasonable range for each parameter. 3 time data ?commands fit time_data ?fit time_data In fitting time data it is important to remember that gnuplot represents time as seconds since 1 January 1970. For example if you wanted to fit a quadratic model for the time dependence of something measured over the course of one day in 2023, you might expect that it could be done using T(x) = a + b*x + c*x*x set xdata time fit T(x) 'hits.dat' using 1:3 via a,b,c This will probably fail, because internally the x values corresponding to that one day will have a range something like [1.67746e+09 : 1.67754e+09]. The fractional change in x across the measured data will be only about 1.e-05 and to guarantee convergence you would probably need many decimal places of accuracy in the initial parameter estimates. One solution is to recast the problem as change in time since the start of measurement. set xdata time # data format "27-02-2023 12:00:00 measurement" timefmt = "%d-%m-%Y %H:%M:%S" set timefmt timefmt t0 = strptime( timefmt, "27-02-2023 00:00:00" ) fit T(x) 'temperature.dat' using ($1-t0):3 via a,b,c This shifts the range of the data to [0 : 86400], which is more tractable. Another possibility in this case is to ignore the date in column 1 and use relative time formats (tH/tM/tS) applied to column 2. set timefmt "%tH:%tM:%tS" fit T(x) 'temperature.dat' using 2:3 via a,b,c 3 tips ?commands fit tips ?fit tips ?tips Here are some tips to keep in mind to get the most out of `fit`. They're not very organized, so you'll have to read them several times until their essence has sunk in. The two forms of the `via` argument to `fit` serve two largely distinct purposes. The `via "file"` form is best used for (possibly unattended) batch operation, where you supply the starting parameter values in a file. The `via var1, var2, ...` form is best used interactively, where the command history mechanism may be used to edit the list of parameters to be fitted or to supply new startup values for the next try. This is particularly useful for hard problems, where a direct fit to all parameters at once won't work without good starting values. To find such, you can iterate several times, fitting only some of the parameters, until the values are close enough to the goal that the final fit to all parameters at once will work. Make sure that there is no mutual dependency among parameters of the function you are fitting. For example, don't try to fit a*exp(x+b), because a*exp(x+b)=a*exp(b)*exp(x). Instead, fit either a*exp(x) or exp(x+b). A technical issue: The larger the ratio of the largest and the smallest absolute parameter values, the slower the fit will converge. If the ratio is close to or above the inverse of the machine floating point precision, it may take next to forever to converge, or refuse to converge at all. You will either have to adapt your function to avoid this, e.g., replace 'parameter' by '1e9*parameter' in the function definition, and divide the starting value by 1e9 or use `set fit prescale` which does this internally according to the parameter starting values. If you can write your function as a linear combination of simple functions weighted by the parameters to be fitted, by all means do so. That helps a lot, because the problem is no longer nonlinear and should converge with only a small number of iterations, perhaps just one. Some prescriptions for analysing data, given in practical experimentation courses, may have you first fit some functions to your data, perhaps in a multi-step process of accounting for several aspects of the underlying theory one by one, and then extract the information you really wanted from the fitting parameters of those functions. With `fit`, this may often be done in one step by writing the model function directly in terms of the desired parameters. Transforming data can also quite often be avoided, though sometimes at the cost of a more difficult fit problem. If you think this contradicts the previous paragraph about simplifying the fit function, you are correct. A "singular matrix" message indicates that this implementation of the Marquardt-Levenberg algorithm can't calculate parameter values for the next iteration. Try different starting values, writing the function in another form, or a simpler function. Finally, a nice quote from the manual of another fitting package (fudgit), that kind of summarizes all these issues: "Nonlinear fitting is an art!" #TeX \newpage 2 function blocks ?commands function ?function blocks ?functionblocks The `function` command signals the definition of a here-document containing a named block of gnuplot code that can be called as a function. As with data blocks, the name of a function block must begin with a '$'. Up to nine named parameters may be specified as part of the definition. These names may be used inside the function block as local variables. See `local` and `scope`. Once the function block is defined, you can invoke it by name anywhere that a normal function could be used. If the return value is not relevant, the function block may be invoked by an "evaluate" command rather than as part of an assignment expression. Example: function $sinc(arg) << EOF if (arg == 0) { return 1.0 } return sin(arg) / arg EOF gnuplot> plot $sinc(x) with lines title "sinc(x) as a function block" It is not necessary to specify a list of named arguments to a function block at the time it is declared. Arguments to the function passed from the command line can be also be accessed from inside the function block as ARGV[1] etc, as they would be for a `call` command. See `ARGV`. This allows defining a function block that can operate on a variable number of arguments. Example: function $max << EOF local max = real("-Inf") if (ARGC == 0) { return NaN } do for [i=1:ARGC] { if (max < ARGV[i]) { max = ARGV[i] } } return max EOF gnuplot> foo = $max( f(A), 2.0, C, Array[3] ) gnuplot> baz = $max( foo, 100. ) The primary motivation for function block support is to allow definition of complicated functions directly in gnuplot. Execution is of course slower than if the same function were coded in C or Fortran, but this is acceptable for many purposes. If execution speed matters then the function can be implemented later as a plugin instead (see `plugins`). A second use for function blocks is to allow execution of gnuplot commands in a context they otherwise could not appear. Suppose for example you want to plot data from two csv files, but one file uses comma-separated fields while the other uses semicolon-separated fields. Normally this property would have been set by a previous `set datafile` command and would have to match all files used by the plot command. However we can define a function block to invoke as a definition immediately before each file is referenced in the plot. function $set_csv(char) << EOF set datafile separator char EOF plot tmp=$set_csv(",") FILE1, tmp=$set_csv(";") FILE2 Limitations: #start #b Data blocks and function blocks cannot be defined inside a function block. #b These commands cannot be executed inside a function block: ## `reset`, `shell`, `!<shell command>`. #b A `plot`, `replot`, `splot`, `refresh`, `stats`, `vfill`, or `fit` command ## is accepted in a function block only if none of those commands is already ## in progress. E.g. you cannot use `stats` in a function block called by a ## `plot` command, you cannot invoke `plot` from inside a `fit` command, etc. #end A non-trivial example of using function blocks to implement and plot a 15-term Lanczos approximation for the complex lngamma function is provided in the demo collection as ^ <a href="https://www.apklas.com?arsae=http%3A%2F%2Fwww.gnuplot.info%2Fdemo_6.0%2Ffunction_block.html" target="_parent"> function_block.dem ^ </a> The function block implementation is slower by a factor of roughly 25 compared to the built-in lnGamma function using the same algorithm coded directly in C. Nevertheless it is still fast enough for 3D interactive rotation. #TeX The function definitions used in that demo are show below. #TeX \newline #TeX \begin{center} #TeX \begin{minipage}{5in} #TeX { #TeX Function block implementation of $log\Gamma(z)$ using a 15-term Lanczos approximation #TeX \hrule #TeX ~\newline #TeX \small #TeX \begin{verbatim} #TeX array coef[15] = [ ... ] #TeX #TeX function $Lanczos(z) << EOD #TeX local Sum = coef[1] + sum [k=2:15] coef[k] / (z + k - 1) #TeX local temp = z + 671./128. #TeX temp = (z + 0.5) * log(temp) - temp #TeX temp = temp + log( sqrt(2*pi) * Sum/z ) #TeX return temp #TeX EOD #TeX #TeX function $Reflect(z) << EOD #TeX local w = $Lanczos(1.0 - z) #TeX local temp = log( sin(pi * z) ) #TeX return log(pi) - (w + temp) #TeX EOD #TeX #TeX my_lngamma(z) = (z == 0) ? NaN : (real(z) < 0.5) ? $Reflect(z) : $Lanczos(z) #TeX \end{verbatim} #TeX \hrule #TeX } #TeX \end{minipage} #TeX \end{center} Use of function blocks is EXPERIMENTAL. Details may change before inclusion in a release version. #TeX \newpage 2 help ?commands help ?help The `help` command displays built-in help. To specify information on a particular topic use the syntax: help {<topic>} If <topic> is not specified, a short message is printed about `gnuplot`. After help for the requested topic is given, a menu of subtopics is given; help for a subtopic may be requested by typing its name, extending the help request. After that subtopic has been printed, the request may be extended again or you may go back one level to the previous topic. Eventually, the `gnuplot` command line will return. If a question mark (?) is given as the topic, the list of topics currently available is printed on the screen. 2 history ?commands history ?history The `history` command prints or saves previous commands in the history list, or reexecutes a previous entry in the list. To modify the behavior of this command or the location of the saved history file, see `set history`. Input lines with `history` as their first command are not stored in the command history. Examples: history # show the complete history history 5 # show last 5 entries in the history history quiet 5 # show last 5 entries without entry numbers history "hist.gp" # write the complete history to file hist.gp history "hist.gp" append # append the complete history to file hist.gp history 10 "hist.gp" # write last 10 commands to file hist.gp history 10 "|head -5 >>diary.gp" # write 5 history commands using pipe history ?load # show all history entries starting with "load" history ?"set c" # like above, several words enclosed in quotes hist !"set xr" # like above, several words enclosed in quotes hist !55 # reexecute the command at history entry 55 2 if ?commands if ?if Syntax: if (<condition>) { <commands>; <commands> <commands> } else if (<condition>) { <commands> } else { <commands> } This version of gnuplot supports block-structured if/else statements. If the keyword `if` or `else` is immediately followed by an opening "{", then conditional execution applies to all statements, possibly on multiple input lines, until a matching "}" terminates the block. If commands may be nested. Prior to gnuplot version 5 the scope of if/else commands was limited to a single input line. Now a multi-line clause may be enclosed in curly brackets. The old syntax is still honored but cannot be used inside a bracketed clause. Old syntax: if (<condition>) <command-line> [; else if (<condition>) ...; else ...] If no opening "{" follows the `if` keyword, the command(s) in <command-line> will be executed if <condition> is true (non-zero) or skipped if <condition> is false (zero). Either case will consume commands on the input line until the end of the line or an occurrence of `else`. Note that use of `;` to allow multiple commands on the same line will _not_ end the conditionalized commands. 2 for ?for The `plot`, `splot`, `set` and `unset` commands may optionally contain an iteration clause. This has the effect of executing the basic command multiple times, each time re-evaluating any expressions that make use of the iteration control variable. Iteration of arbitrary command sequences can be requested using the `do` command. Two forms of iteration clause are currently supported: for [intvar = start:end{:increment}] for [stringvar in "A B C D"] Examples: plot for [filename in "A.dat B.dat C.dat"] filename using 1:2 with lines plot for [basename in "A B C"] basename.".dat" using 1:2 with lines set for [i = 1:10] style line i lc rgb "blue" unset for [tag = 100:200] label tag Nested iteration is supported: set for [i=1:9] for [j=1:9] label i*10+j sprintf("%d",i*10+j) at i,j See additional documentation for `iteration`, `do`. 2 import ?commands import ?import =plugins The `import` command associates a user-defined function name with a function exported by an external shared object. This constitutes a plugin mechanism that extends the set of functions available in gnuplot. Syntax: import func(x[,y,z,...]) from "sharedobj[:symbol]" Examples: # make the function myfun, exported by "mylib.so" or "mylib.dll" # available for plotting or numerical calculation in gnuplot import myfun(x) from "mylib" import myfun(x) from "mylib:myfun" # same as above # make the function theirfun, defined in "theirlib.so" or "theirlib.dll" # available under a different name import myfun(x,y,z) from "theirlib:theirfun" The program extends the name given for the shared object by either ".so" or ".dll" depending on the operating system, and searches for it first as a full path name and then as a path relative to the current directory. The operating system itself may also search any directories in LD_LIBRARY_PATH or DYLD_LIBRARY_PATH. See `plugins`. 2 load ?commands load ?load The `load` command executes each line of the specified input file as if it had been typed in interactively. Files created by the `save` command can later be `load`ed. Any text file containing valid gnuplot commands can be executed by a `load` command. Files being loaded may themselves contain `load` or `call` commands. To pass arguments to a loaded file, see `call`. Syntax: load "<input-file>" load $datablock The name of the input file must be enclosed in quotes. The special filename "-" may be used to `load` commands from standard input. This allows a `gnuplot` command file to accept some commands from standard input. Please see help for `batch/interactive` for more details. On systems that support a popen function, the load file can be read from a pipe by starting the file name with a '<'. Examples: load 'work.gnu' load "func.dat" load "< loadfile_generator.sh" The `load` command is performed implicitly on any file names given as arguments to `gnuplot`. These are loaded in the order specified, and then `gnuplot` exits. EXPERIMENTAL: It is also possible to execute commands from lines of text stored internally. See `function blocks`. A function block may be defined in-line or in an external file. Once the function block has been defined the commands may be executed repeatedly using `evaluate` on the internal copy rather than reloading the file. 2 local ?local ?commands local Syntax: local foo = <expression> local array foo[size] The `local` keyword introduces declaration of a variable whose scope is limited to the execution of the code block in which it is declared. Declaration is optional, but without it all variables are global. If the name of a local variable duplicates the name of a global variable, the global variable is shadowed until exit from the local scope. See `scope`. Local declarations may be used to prevent a global variable from being unintentionally overwritten by a `call` or `load` statement. They are particularly useful inside a function block. The `local` command is also valid inside the code block in curly brackets following an `if`, `else`, `do for`, or `while` statement. Example: Suppose you want to write a script "plot_all_data.gp" containing commands that plot a bunch of data sets. You want to call this convenience script from the command line or from other scripts without worrying that it trashes any variables with names "file" or "files" or "dataset" or "outfile". The variable "file" is inherently local because it is an iteration variable (see `scope`) but the other three names need keyword `local` to protect them. plot_all_data.gp: local files = system("ls -1 *.dat") do for [file in files] { local dataset = file[1:strstrt(file,".dat")-1] local outfile = dataset . ".png" set output outfile plot file with lines title dataset } unset output 2 lower See `raise`. 2 pause ?commands pause ?pause ?pause mouse The `pause` command displays any text associated with the command and then waits a specified amount of time or until the carriage return is pressed. `pause` is especially useful in conjunction with `load` files. Syntax: pause <time> {"<string>"} pause mouse {<endcondition>}{, <endcondition>} {"<string>"} pause mouse close <time> may be any constant or floating-point expression. `pause -1` will wait until a carriage return is hit, zero (0) won't pause at all, and a positive number will wait the specified number of seconds. If the current terminal supports `mousing`, then `pause mouse` will terminate on either a mouse click or on ctrl-C. For all other terminals, or if mousing is not active, `pause mouse` is equivalent to `pause -1`. If one or more end conditions are given after `pause mouse`, then any one of the conditions will terminate the pause. The possible end conditions are `keypress`, `button1`, `button2`, `button3`, `close`, and `any`. If the pause terminates on a keypress, then the ascii value of the key pressed is returned in MOUSE_KEY. The character itself is returned as a one character string in MOUSE_CHAR. Hotkeys (bind command) are disabled if keypress is one of the end conditions. Zooming is disabled if button3 is one of the end conditions. In all cases the coordinates of the mouse are returned in variables MOUSE_X, MOUSE_Y, MOUSE_X2, MOUSE_Y2. See `mouse variables`. Note: Since `pause` communicates with the operating system rather than the graphics, it may behave differently with different device drivers (depending upon how text and graphics are mixed). Examples: pause -1 # Wait until a carriage return is hit pause 3 # Wait three seconds pause -1 "Hit return to continue" pause 10 "Isn't this pretty? It's a cubic spline." pause mouse "Click any mouse button on selected data point" pause mouse keypress "Type a letter from A-F in the active window" pause mouse button1,keypress pause mouse any "Any key or button will terminate" The variant "pause mouse key" will resume after any keypress in the active plot window. If you want to wait for a particular key to be pressed, you can use a loop such as: print "I will resume after you hit the Tab key in the plot window" plot <something> pause mouse key while (MOUSE_KEY != 9) { pause mouse key } 3 pause mouse close ?commands pause mouse close ?pause mouse close ?pause close The command `pause mouse close` is a specific example of pausing to wait for an external event. In this case the program waits for a "close" event from the plot window. Exactly how to generate such an event varies with your desktop environment and configuration, but usually you can close the plot window by clicking on some widget on the window border or by typing a hot-key sequence such as <alt><f4> or <ctrl>q. If you are unsure whether a suitable widget or hot-key is available to the user, you may also want to define a hot-key sequence using gnuplot's own mechanism. See `bind`. The command sequence below may be useful when running gnuplot from a script rather than from the command line. plot <...whatever...> bind all "alt-End" "exit gnuplot" pause mouse close 3 pseudo-mousing during pause ?commands pause pseudo-mousing ?pseudo-mousing Some terminals use the same window for text entry and graphical display, including terminal types `dumb`, `sixel`, `kitty`, and `domterm`. These terminals do not currently support mousing per se, but during a `pause mouse` command they interpret keystrokes in the same way that a mousing terminal would. I.e. `l` toggles log-scale axes, `a` autoscales the current plot, left/right/up/down arrow keys change the view angle of 3D plots and perform incremental pan/zoom steps for 2D plots. `h` displays a list of key bindings. A carriage return terminates the `pause` and restores normal command line processing. 2 plot ?commands plot ?plot `plot` and `splot` are the primary commands for drawing plots with `gnuplot`. They offer many different graphical representations for functions and data. `plot` is used to draw 2D functions and data. `splot` draws 2D projections of 3D surfaces and data. Syntax: plot {<ranges>} <plot-element> {, <plot-element>, <plot-element>} Each plot element consists of a definition, a function, or a data source together with optional properties or modifiers: plot-element: {<iteration>} <definition> | {sampling-range} <function> | <data source> | keyentry {axes <axes>} {<title-spec>} {with <style>} The graphical representation of each plot element is determined by the keyword `with`, e.g. `with lines` or `with boxplot`. See `plotting styles`. The data to be plotted is either generated by a function (two functions if in parametric mode), read from a data file, read from a named data block that was defined previously, or extracted from an array. Multiple datafiles, data blocks, arrays, and/or functions may be plotted in a single plot command separated by commas. See `data`, `inline data`, `functions`. A plot-element that contains the definition of a function or variable does not create any visible output, see third example below. Examples: plot sin(x) plot sin(x), cos(x) plot f(x) = sin(x*a), a = .2, f(x), a = .4, f(x) plot "datafile.1" with lines, "datafile.2" with points plot [t=1:10] [-pi:pi*2] tan(t), \ "data.1" using (tan($2)):($3/$4) smooth csplines \ axes x1y2 notitle with lines 5 plot for [datafile in "spinach.dat broccoli.dat"] datafile See also `show plot`. 3 axes ?commands plot axes ?plot axes ?axes There are four possible sets of axes available; the keyword <axes> is used to select the axes for which a particular line should be scaled. `x1y1` refers to the axes on the bottom and left; `x2y2` to those on the top and right; `x1y2` to those on the bottom and right; and `x2y1` to those on the top and left. Ranges specified on the `plot` command apply only to the first set of axes (bottom left). 3 binary ?binary ?data binary ?datafile binary ?plot data binary BINARY DATA FILES: It is necessary to provide the keyword `binary` after the filename. Adequate details of the file format must be given on the command line or extracted from the file itself for a supported binary `filetype`. In particular, there are two structures for binary files, binary matrix format and binary general format. The `binary matrix` format contains a two dimensional array of 32 bit IEEE float values plus an additional column and row of coordinate values. In the `using` specifier of a plot command, column 1 refers to the matrix row coordinate, column 2 refers to the matrix column coordinate, and column 3 refers to the value stored in the array at those coordinates. The `binary general` format contains an arbitrary number of columns for which information must be specified at the command line. For example, `array`, `record`, `format` and `using` can indicate the size, format and dimension of data. There are a variety of useful commands for skipping file headers and changing endianess. There are a set of commands for positioning and translating data since often coordinates are not part of the file when uniform sampling is inherent in the data. Unlike reading from a text or matrix binary file, general binary does not treat the generated columns as 1, 2 or 3 in the `using` list. Instead column 1 refers to column 1 of the file, or as specified in the `format` list. There are global default settings for the various binary options which may be set using the same syntax as the options when used as part of the `(s)plot <filename> binary ...` command. This syntax is `set datafile binary ...`. The general rule is that common command-line specified parameters override file-extracted parameters which override default parameters. `Binary matrix` is the default binary format when no keywords specific to `binary general` are given, i.e., `array`, `record`, `format`, `filetype`. General binary data can be entered at the command line via the special file name '-'. However, this is intended for use through a pipe where programs can exchange binary data, not for keyboards. There is no "end of record" character for binary data. Gnuplot continues reading from a pipe until it has read the number of points declared in the `array` qualifier. See `binary matrix` or `binary general` for more details. The `index` keyword is not supported, since the file format allows only one surface per file. The `every` and `using` specifiers are supported. `using` operates as if the data were read in the above triplet form. ^ <a href="http://www.gnuplot.info/demo/binary.html"> Binary File Splot Demo. ^ </style></title-spec></axes></data></function></definition></iteration></plot-element></plot-element></plot-element></ranges></ctrl></f4></alt></something></time></string></endcondition></endcondition></string></time></expression></input-file></condition></condition></command-line></condition></command-line></condition></commands></commands></condition></commands></commands></commands></condition></topic></topic></shell></datafile></ranges></expression></max></min></var2></var1></parameter></var2></var1></datafile></expression></ranges></value></integer></commands></commands></iteration-spec></param-1></param-9></param-3></param-2></param-1></directory-name></p></line></n></colorspec></colorspec></fillstyle></y></x></radius></line></xpos></p></y-offset></baseline></data></x-coord></x-coord></x-coord></fillstyle></linetype></colorspec>

An Interactive Plotting Program

Thomas Williams & Colin Kelley

Version 6 organized by Ethan A Merritt

Major contributors (alphabetic order):
^
^ Hans-Bernhard Broeker, John Campbell,
^ Robert Cunningham, David Denholm,
^ Gershon Elber, Roger Fearick,
^ Carsten Grammes, Lucas Hart, Lars Hecking,
^ PÃ©ter JuhÃ¡sz, Thomas Koenig, David Kotz,
^ Ed Kubaitis, Russell Lang, TimothÃ©e Lecomte,
^ Alexander Lehmann, Alexander Mai, Bastian MÃ¤rkisch,
^ Tatsuro Matsuoka, Ethan A Merritt, Petr MikulÃk,
^ Hiroki Motoyoshi, Carsten Steger, Shigeharu Takeno,
^ Tom Tkacik, Jos Van der Woude,
^ James R. Van Zandt, Alex Woo, Johannes Zellner
^

Mailing list for comments: [email protected]
^ Gnuplot home page
^ Issue trackers: ^ bugs ^ feature requests ^

This manual was originally prepared by Dick Crawford

^ 2 Copyright ?copyright ?license Copyright (C) 1986 - 1993, 1998, 2004, 2007 Thomas Williams, Colin Kelley Copyright (C) 2004-2023 various authors Permission to use, copy, and distribute this software and its documentation for any purpose with or without fee is hereby granted, provided that the above copyright notice appear in all copies and that both that copyright notice and this permission notice appear in supporting documentation. Permission to modify the software is granted, but not the right to distribute the complete modified source code. Modifications are to be distributed as patches to the released version. Permission to distribute binaries produced by compiling modified sources is granted, provided you 1. distribute the corresponding source modifications from the released version in the form of a patch file along with the binaries, 2. add special version identification to distinguish your version in addition to the base release version number, 3. provide your name and address as the primary contact for the support of your modified version, and 4. retain our contact information in regard to use of the base software. Permission to distribute the released version of the source code along with corresponding source modifications in the form of a patch file is granted with same provisions 2 through 4 for binary distributions. This software is provided "as is" without express or implied warranty to the extent permitted by applicable law. AUTHORS Original Software: Thomas Williams, Colin Kelley. Gnuplot 2.0 additions: Russell Lang, Dave Kotz, John Campbell. Gnuplot 3.0 additions: Gershon Elber and many others. Gnuplot 4.0 and subsequent releases: See list of contributors at head of this document. 2 Introduction ?introduction ? `Gnuplot` is a portable command-line driven graphing utility for Linux, OS/2, MS Windows, macOS, and many other platforms. The source code is copyrighted but freely distributed (i.e., you don't have to pay for it). It was originally created to allow scientists and students to visualize mathematical functions and data interactively, but has grown to support many non-interactive uses such as web scripting. It is also used as a plotting engine by third-party applications like Octave. Gnuplot has been supported and under active development since 1986. Gnuplot can generate many types of plot in 2D and 3D. It can draw using lines, points, boxes, contours, vector fields, images, surfaces, and associated text. It also supports specialized graphs such as heat maps, spider plots, polar projection, histograms, boxplots, bee swarm plots, and nonlinear coordinates. Gnuplot supports many different types of output: interactive screen terminals (with mouse and hotkey input), direct output to pen plotters or modern printers, and output to many file formats (eps, emf, fig, jpeg, LaTeX, pdf, png, postscript, ...). Gnuplot is easily extensible to include new output modes. A recent example is support for webp animation. Mouseable plots embedded in web pages can be generated using the svg or HTML5 canvas terminal drivers. The command language of `gnuplot` is case sensitive, i.e. commands and function names written in lowercase are not the same as those written in capitals. All command names may be abbreviated as long as the abbreviation is not ambiguous. Any number of commands may appear on a line, separated by semicolons (;). Strings may be set off by either single or double quotes, although there are some subtle differences. See `syntax` and `quotes` for more details. Example: set title "My First Plot"; plot 'data'; print "all done!" Commands may extend over several input lines by ending each line but the last with a backslash (\). The backslash must be the _last_ character on each line. The effect is as if the backslash and newline were not there. That is, no white space is implied, nor is a comment terminated. Therefore, commenting out a continued line comments out the entire command (see `comments`). But note that if an error occurs somewhere on a multi-line command, the parser may not be able to locate precisely where the error is and in that case will not necessarily point to the correct line. In this document, curly braces ({}) denote optional arguments and a vertical bar (|) separates mutually exclusive choices. `Gnuplot` keywords or `help` topics are indicated by backquotes or `boldface` (where available). Angle brackets (<>) are used to mark replaceable tokens. In many cases, a default value of the token will be taken for optional arguments if the token is omitted, but these cases are not always denoted with braces around the angle brackets. For built-in help on any topic, type `help` followed by the name of the topic or `help ?` to get a menu of available topics. A large set of demo plots is available on the web page ^ http://www.gnuplot.info/demo/ ^ When run from command line, gnuplot is invoked using the syntax gnuplot {OPTIONS} file1 file2 ... where file1, file2, etc. are input files as in the `load` command. Options interpreted by gnuplot may come anywhere on the line. Files are executed in the order specified, as are commands supplied by the -e option, for example gnuplot file1.in -e "reset" file2.in The special filename "-" is used to force reading from stdin. `Gnuplot` exits after the last file is processed. If no load files are named, `Gnuplot` takes interactive input from stdin. See help `batch/interactive` for more details. See `command-line-options` for more details, or type gnuplot --help In sessions with an interactive plot window you can hit 'h' anywhere on the plot for help about `hotkeys` and `mousing` features. 2 Seeking-assistance / Bugs ?help-desk ?faq ?FAQ ?bugs ?seeking-assistance The canonical gnuplot home page can be found at ^ http://www.gnuplot.info ^ Before seeking help, please check file FAQ.pdf or the above website for a ^ FAQ (Frequently Asked Questions) list. ^ Another resource for help with specific plotting problems (not bugs) is https://stackoverflow.com/questions/tagged/gnuplot Bug reports and feature requests should be uploaded to the trackers at https://sourceforge.net/p/gnuplot/_list/tickets Please check previous reports to see if the bug you want to report has already been fixed in a newer version. When reporting a bug or posting a question, please include full details of the gnuplot version, the terminal type, and the operating system. A short self-contained script demonstrating the problem is very helpful. Instructions for subscribing to gnuplot mailing lists may be found via the gnuplot development website ^ http://sourceforge.net/projects/gnuplot ^ Please note that before you write to any of the gnuplot mailing lists you must first subscribe to the list. This helps reduce the amount of spam. The address for mailing to list members is: [email protected] A mailing list for those interested in the development version of gnuplot is: [email protected] 2 New features in version 6 ?new version_6 ?new ?version Version 6 is the latest major release in a history of gnuplot development dating back to 1986. It follows major version 5 (2015) and subsequent minor version releases 5.2 (2017) and 5.4 (2020). Development continues in a separate unreleased branch in the project git repository on SourceForge. Some features described in this document are present only if chosen and configured at the time gnuplot is compiled from source. To determine what configuration options were used to build the particular copy of gnuplot you are running, type `show version long`. 3 Function blocks and scoped variables ?new function blocks This version of gnuplot introduces a mechanism for invoking a block of standard gnuplot commands as a callable function. A function block can accept from 0 to 9 parameters and returns a value. Function blocks can be used to calculate and assign a new value to a variable, to combine with other functions and operators, or to perform a repetitive task preparing data. There are three components to this mechanism. See `local`, `scope`, `function blocks`, `return`. #start #b The `local` qualifier allows optional declaration of a variable or array ## whose scope is limited to the duration of execution of the program unit in ## which it is found. These units currently include execution of a ## `load` or `call` statement, function block evaluation, and the code block ## in curly brackets following an `if`, `else`, `do for`, or `while` statement. ## If the name of a local variable duplicates the name of a global variable, ## the global variable is shadowed until exit from the local scope. #b The `function` command declares a named function block (effectively an ## array of strings) containing gnuplot commands. When the function block ## is invoked, commands are executed successively until the end of the block ## or until a `return` command is encountered. #b The `return ` command terminates execution of a function block. ## The result of evaluating is returned as the value of the ## function. Anywhere outside a function block `return` acts like `exit`. #end Please see `function_block.dem` for an example of using this mechanism to define and plot a non-trivial function that is too complicated for a simple one-line definition `f(x) = ...`. 3 Special and complex-valued functions ?new math Gnuplot 6 provides an expanded set of complex-valued functions and updated versions of some functions that were present in earlier versions. #start #b New: Riemann zeta function with complex domain and range. See `zeta`. #b Updated lower incomplete gamma function with improved domain and precision. ## Complex arguments accepted. ## See `igamma`. #b New upper incomplete gamma function (real arguments only). ## See `uigamma`. #b Updated incomplete beta function with improved domain and precision. ## See `ibeta`. #b New function for the inverse incomplete gamma function. ## See `invigamma`. #b New function for the inverse incomplete beta function. ## See `invibeta`. #b New complex function LambertW(z,k) returns the kth branch of multivalued ## function W_k(z). ^
## Note that the older function lambertw(x) = real(LambertW( real(z), 0 )). ## See `LambertW`. #b New complex function lnGamma(z). ## Note that existing function lgamma(x) = real(lnGamma(real(z)). ## See `lnGamma`. #b Complex function conj(z) returns the complex conjugate of z. #b Synchrotron function F(x), see `SynchrotronF`. #b acosh(z) domain extended to cover negative real axis. #b asin(z) asinh(z) improved precision for complex arguments. #b Predefined variable I = sqrt(-1) = {0,1} for convenience. ^
## This is useful because gnuplot does not accept {a,b} as a valid complex ## constant but does accept (a + b*I) as a valid complex expression. #end Additional special functions are supported if a suitable external library is found at build time. See `special_functions`. #start #b Complex Bessel functions IÎ½(z), JÎ½(z), KÎ½(z), YÎ½(z) of order Î½ (real) ## with complex argument z. See `BesselK`. #b Complex Hankel functions H1Î½(z), H2Î½(z) of order Î½ with complex z. ## See `BesselH1`. #b Complex Airy functions Ai(z), Bi(z). #b Complex exponential integral of order n. See `expint`. #b Fresnel integrals C(x) and S(x). See `FresnelC`. #b Function `VP_fwhm(sigma,gamma)` returns the full width at half maximum ## of the Voigt profile. See `VP`, `VP_fwhm`. #end 3 New plot styles ?new styles #start #b The plot style `with surface` works in 2D polar coordinates to produce ## a solid-fill gridded representation of the plane, colored by weighted ## contributions from an arbitrary set of input points. This is analogous to ## the use of `dgrid3d` and style `with pm3d` to produce a 3D gridded surface. ## See `set polar grid` and `polar heatmap`. #b New 2D plot style `with sectors` is an alternative to generating a full ## polar gridded surface. For each input data point it generates a single ## annular wedge in a conceptual polar grid. Unlike polar mode `with surface` ## it can be used in either a polar or cartesian coordinate graph. #b New 2D plot style `with hsteps` allows construction of step-like plots with ## a variety of representations in addition to those offered by existing styles ## `steps`, `histeps`, `fsteps`, and `fillsteps`. See `hsteps`. #b Plot style `with lines` now has a filter option `sharpen`. This filter ## detects spikes in a function plot that appear truncated in the output ## because the peak lies between two x-coordinates at which the function has ## been sampled. It adds a new sample point at the location of each such peak. ## See `filters`. #b Although it is not strictly speaking a new plot style, the combination ## of the concave hull filter with along-path smoothing of filled areas ## allows creation of 'blobby region' plots showing, for example, ## the extents of overlapping data clusters. See `concavehull`. #b 3D plot style `with pm3d` accepts an optional modifier `zclip [zmin:zmax]` ## that selects only a slice of the full surface. Successive plots with ## incremental changes to the clipping limits can be used to animate a ## cross-sectional cutaway view in 3D or to create a filled area contour map. ## This is automated by a new plot style `with contourfill`, that is ## particularly useful in 2D projection. See `set contourfill`. #end D polargrid 4 DB D windrose 1 D sectors 4 DB D sharpen 1 D iris 2 DB D contourfill 4 DB D logic_timing 1 D rank_sequence 1 3 Hulls, masks, and smoothing ?new hulls #start #b A cluster of 2D points can be replaced by its bounding polygon using the ## new filter `convexhull`. A path-smoothed bounding curve can be plotted ## as a filled area using "convexhull smooth path with filledcurves". ## See `convexhull`. #b An alternative experimental filter `concavehull` generates a bounding ## polygon that is not necessarily convex; instead it forms a Ï‡-shape ## determined by a characteristic length parameter that controls the degree ## of concavity. This essentially draws a blob around the data points. ## See `concavehull`. #b A convex hull or other polygon can be used as a mask to display only ## selected portions of a pm3d surface or an image plot. ## See new plot style `with mask` (defines a mask) and keyword `mask` ## (applies the mask to a subsequent plot component). #b curve smoothing using along-path cubic splines suitable for closed curves ## or for 2D curves that are not monotonic on x. See `smooth path`. ## This allows smoothing of hulls and masks. #b cubic spline smoothing of 3D lines. See `splot smooth csplines` #b Smoothing options apply to plotting `with filledcurves` {above|below|between}. #b New keyword `period` for smoothing periodic data. See `smooth kdensity`. #end D convex_hull 2 D mask_pm3d 3 D smooth_path 2 3 Named palettes ?new colormaps #start #b The current palette can be saved to a named colormap for future use. ## See `set colormap`. #b pm3d and image plots can specify a previously saved palette by name. ## This permits the use of multiple palettes in a single plot command. ## See `colorspec palette`. #b Named palette colormaps can be manipulated as arrays of 32-bit ARGB ## color values. This permits addition of alpha-channel values or other ## modifications not easily specified in a `set palette` command. #b There is a new predefined color scheme `set palette viridis`. #b Palettes read from a file or datablock (`set palette file`) may be specified ## either using fractional color components or 24-bit packed RGB values. #end D named_palettes 4 D viridis 1 3 New data formats ?new data_formats #start #b The `sparse matrix=(cols,rows)` option to `plot` and `splot` generates ## a uniform pixel grid into which individual pixel values may be loaded in ## any order. This is useful for plotting heat maps from incomplete data. ## See `sparse`. #b During input of non-uniform matrix data, column(0) now returns the linear ## ordering of matrix elements. I.e. for element A[i,j] in an MxN matrix A, ## column(0)/M gives the row index i, and column(0)%M gives the column index j. #end 3 New built-in functions and array operations ?new built-in functions #start #b `palette(z)` returns the current RGB palette color mapping z into cbrange. #b `rgbcolor("name")` returns the 32bit ARGB value for a named color. #b `index( Array, element )` returns the first index `i` for which ## Array[i] is equal to element. See `arrays`. #b User-defined functions allow an array as a parameter. ^
## Example: dot(A,B) = sum [i=1:|A|] A[i]*B[i] #b Array slices are generated by appending a range to the array name. ## Array[n] is single element. Array[n:n+5] is a six element slice of ## the original array. See `arrays`, `slice`. #b `split("string", "separator")` unpacks the fields in a string into ## an array of strings. See `split`. #b `join(array, "separator")` is the complement to `split`. It concatenates ## the elements of a string array into a single string with field separators. ## See `join`. #b `stats ` yields a testable value. See `stats test`. #b `stats $vgrid` finds min/max/mean/stddev of voxels in grid #end 3 Program control flow ?control flow #start #b New syntax `if ... else if ... else ...` #b XDG base directory conventions for configuration preferences are supported. ## The program reads initial commands from $XDG_CONFIG_HOME/gnuplot/gnuplotrc. ## Session command history is saved to $XDG_STATE_HOME/gnuplot_history. ## If these files are not found, $HOME/.gnuplot and $HOME/.gnuplot_history ## are used as in previous gnuplot versions. #b `unset warnings` suppresses output of warning messages to the console. #b Exception handling for the "fit" command. Control always returns to the ## next line of input, even in the case of fit errors. On return, FIT_ERROR is ## non-zero if an error occurred. This allows scripted recovery from a bad fit. ## See `fit error_recovery`. #end 3 New terminals and terminal options ?new terminals #start #b New terminals `kittygd` and `kittycairo` provide in-window graphics for ## terminal emulators that support the kitty protocol. Kitty is an alternative ## to sixel graphics that offers full 24-bit RGB color. See `kittycairo`. #b New terminal `block` for text-mode pseudo-graphics uses Unicode ## block or Braille characters to offer improved resolution compared ## to the `dumb` or `caca` terminals. #b New terminal `webp` generates a single frame or an animation sequence ## using webp encoding. Frames are generated using pngcairo, then ## encoded through the WebPAnimEncoder API exported by libwebp and libwebpmux. #b Terminals that use the same window for text entry and graphical display, ## including `dumb`, `sixel`, `kitty`, and `block`, now respond to keyboard ## input during a `pause mouse` command. While paused, they interpret keystrokes ## in the same way that a mousing terminal would. See `pseudo-mousing`. ## For example the left/right/up/down arrow keys change the view angle of 3D ## plots and perform incremental pan/zoom steps for 2D plots. #end 3 Watchpoints ?new watchpoints Watchpoints are target values associated with individual plots in a graph. As that plot is drawn, each component line segment is monitored to see if its endpoints bracket the target value of a watchpoint coordinate (x, y, or z) or function f(x,y). If a match is found, the [x,y] coordinates of the match point are saved for later use. See `watchpoints`. Possible uses include #start #b Find the intersection points of two curves #b Find zeros of a function #b Find and notate where a dependent variable (y or z) or function f(x,y) ## crosses a threshold value #b Use the mouse to track values along multiple plots simultaneously #end 3 Week-date time support ?new week-date time The Covid-19 pandemic of 2020/2021 generated increased interest in plotting epidemiological data, which is often tabulated using a "week date" reporting convention. Deficiencies with gnuplot support for this convention were remedied and the support for week-date time was extended. #start #b Time specifier format %W has been brought into accord with the ## ISO 8601 week date standard. #b Time specifier format %U has been brought into accord with the ## CDC/MMWR week date standard. #b New function `tm_week(time, std)` returns ISO or CDC standard week of year. #b New function `weekdate_iso(year, week, day)` converts ISO standard week date ## to calendar time. #b New function `weekdate_cdc(year, week, day)` converts CDC standard week date ## to calendar time. #end D epi_data 1 3 Other new features ?new features #start #b `Time units for setting major and minor tics.` ## Both major and minor tics along a time axis now accept tic intervals given ## in units of minutes/hours/days/weeks/months/years. ## See `set xtics`, `set mxtics time`. #b The character sequence $# in a `using` specifier evaluates to the total ## number of columns available in the current line of data. For example ## "plot FOO using 0:(column($# - 1))" plots the last-but-one field of each row. #b keyword `binvalue=avg` plots the average, rather than the sum, of binned data. #b `set colorbox bottom` places a horizontal color box underneath the plot ## rather than a vertical box on the right. #b Improved rendering of intersecting pm3d surfaces - overlapping surface tiles ## are split into two pieces along the line of intersection so that tiles ## from one surface do not incorrectly protrude though the other surface. #b User-controlled spotlight added to the pm3d lighting model. ## See `set pm3d spotlight`. #b New options to force total key width and number of columns. See `key layout`. #b `set pm3d border retrace` draws a border around each pm3d quadrangle in the ## same color as the filled area. In principle this should have no visible ## effect, but it prevents some display modes like glitchy pdf or postscript ## viewers from introducing aliasing artifacts. #b `set isotropic` adjusts the axis scaling in both 2D and 3D plots such that ## the x, y, and z axes all have the same scale. #b Change: Text rotation angle is not limited to integral degrees. #b Special (non-numerical) linetypes `lt nodraw`, `lt black`, `lt bgnd` ## See `special_linetypes`. #b Data-driven color assignments in histogram plots. See `histograms colors`. #b The position of the key box can be manually tweaked by specifying an ## offset to be added to whatever position the program would otherwise use. ## See `set key offset`. #end 3 Brief summary of features introduced in version 5 ?new version_5 ?version_5 4 Features introduced in 5.4 ?new version_5 version_5.4 ?version_5 version_5.4 #start #b Expressions and functions use 64-bit integer arithmetic. See `integer` #b 2D plot styles `polygons`, `spiderplot`, `arrows` #b 3D plot styles `boxes`, `circles`, `polygons`, `isosurface` and ## other representations of gridded voxel data #b Data preprocessing filter `zsort` #b Construction of customized keys using `keyentry` #b New LaTeX terminal pict2e supersedes older terminals `latex`, `emtex`, `eepic`, ## and `tpic`. The older terminals are no longer built by default #b `set pixmap` imports a png/jpeg/gif image as a pixmap that can be scaled and ## positioned anywhere in a plot or on the page #b Enhanced text mode accepts \U+xxxx (xxxx is a 4 or 5 character hexadecimal) ## as representing a Unicode code point that is converted to the corresponding ## UTF-8 byte sequence on output #b Revised syntax for `with parallelaxes` allows convenient iteration inside the ## plot command, similar to plot styles `histogram` and `spiderplot` #end 4 Features introduced in 5.2 ?new version_5 version_5.2 ?version_5 version_5.2 #start #b Nonlinear coordinate systems (see `set nonlinear`) #b Automated binning of data (see `bins`) #b 2D beeswarm plots. See `set jitter` #b 3D plot style `zerrorfill` #b 3D lighting model provides shading and specular highlighted (see `lighting`). #b Array data type, associated commands and operators. See `arrays`. #b New terminals `sixelgd`, `domterm` #b New format descriptors tH tM tS handle relative times (interval lengths). ## See `time_specifiers`. #end 4 Features introduced in 5.0 ?new version_5 version_5.0 ?version_5 version_5.0 #start #b Terminal independent dash types. #b The default sequence of colors used for successive elements in a plot is ## more easily distinguished by users with color-vision defects. #b New plot types `with parallelaxes`, `with table`. #b Hypertext labels activated by a mouse-over event. #b Explicit sampling ranges in 2D and 3D function plots and pseudofiles ## '+' and '++'. #b Plugin support through new command `import` that attaches a user-defined ## function name to a function provided by an external shared object. #end 2 Differences between versions 5 and 6 Some changes introduced in version 5 could cause certain scripts written for earlier versions of gnuplot to fail or to behave differently. There are very few such changes in version 6. 3 Deprecated syntax ?deprecated syntax Deprecated in version 5.4, removed in 6.0 # use of a file containing `reread` to perform iteration N = 0; load "file-containing-reread"; file content: N = N+1 plot func(N,x) pause -1 if (N<5) reread Current equivalent do for [N=1:5] { plot func(N, x) pause -1 } Deprecated in version 5.4, removed in 6.0 set dgrid3d ,,foo # no keyword to indicate meaning of foo Current equivalent set dgrid3d qnorm foo # (example only; qnorm is not the only option) Deprecated in version 5.0, removed in 6.0 set style increment user Current equivalent use "set linetype" to redefine a convenient range of linetypes Deprecated in version 5.0, removed in 6.0 show palette fit2rgbformulae 2 Demos and Online Examples ?demos ?online examples ?examples The `gnuplot` distribution contains a collection of examples in the `demo` directory. You can browse on-line versions of these examples produced by the png, svg, and canvas terminals at ^ http://gnuplot.info/demos ^ The commands that produced each demo plot are shown next to the plot, and the corresponding gnuplot script can be downloaded to serve as a model for generating similar plots. 2 Batch/Interactive Operation ?batch/interactive `Gnuplot` may be executed in either batch or interactive modes, and the two may even be mixed together. Command-line arguments are assumed to be either program options or names of files containing `gnuplot` commands. Each file or command string will be executed in the order specified. The special filename "-" is indicates that commands are to be read from stdin. `Gnuplot` exits after the last file is processed. If no load files and no command strings are specified, `gnuplot` accepts interactive input from stdin. 3 command line options ?command-line-options ?batch/interactive command-line-options Gnuplot accepts the following options on the command line -V, --version -h, --help -p, --persist -d, --default-settings -s, --slow -e "command1; command2; ..." -c scriptfile ARG1 ARG2 ... -p tells the program not to close any remaining interactive plot windows when the program exits. -d tells the program not to execute any private or system initialization (see `initialization`). -s tells the program to wait for slow font initialization on startup. Otherwise it prints an error and continues with bad font metrics. -e "command" tells gnuplot to execute that single command before continuing. -c is equivalent to -e "call scriptfile ARG1 ARG2 ...". See `call`. 3 Examples ?batch/interactive examples To launch an interactive session: gnuplot To execute two command files "input1" and "input2" in batch mode: gnuplot input1 input2 To launch an interactive session after an initialization file "header" and followed by another command file "trailer": gnuplot header - trailer To give `gnuplot` commands directly in the command line, using the "-persist" option so that the plot remains on the screen afterwards: gnuplot -persist -e "set title 'Sine curve'; plot sin(x)" To set user-defined variables a and s prior to executing commands from a file: gnuplot -e "a=2; s='file.png'" input.gpl 2 Canvas size ?canvas size ?canvas ?set term size This documentation uses the term "canvas" to mean the full drawing area available for positioning the plot and associated elements like labels, titles, key, etc. NB: For information about the HTML5 canvas terminal see `set term canvas`. `set term size , ` controls the size of the output file, or "canvas". By default, the plot will fill this canvas. `set size , ` scales the plot itself relative to the size of the canvas. Scale values less than 1 will cause the plot to not fill the entire canvas. Scale values larger than 1 will cause only a portion of the plot to fit on the canvas. Please be aware that setting scale values larger than 1 may cause problems. Example: set size 0.5, 0.5 set term png size 600, 400 set output "figure.png" plot "data" with lines These commands produce an output file "figure.png" that is 600 pixels wide and 400 pixels tall. The plot will fill the lower left quarter of this canvas. Note: In early versions of gnuplot some terminal types used `set size` to control the size of the output canvas. This was deprecated in version 4. 2 Command-line-editing ?line-editing ?editing ?command-line-editing Command-line editing and command history are supported using either an external gnu readline library, an external BSD libedit library, or a built-in equivalent. This choice is a configuration option at the time gnuplot is built. The editing commands of the built-in version are given below. Please note that the action of the DEL key is system-dependent. The gnu readline and BSD libedit libraries have their own documentation. @start table - first is interactive cleartext form `Line-editing`: ^B moves back a single character. ^F moves forward a single character. ^A moves to the beginning of the line. ^E moves to the end of the line. ^H deletes the previous character. DEL deletes the current character. ^D deletes current character, sends EOF if the line is empty. ^K deletes from current position to the end of line. ^L redraws line in case it gets trashed. ^U deletes the entire line. ^W deletes previous word. ^V inhibits the interpretation of the following key as editing command. TAB performs filename-completion. `History`: ^P moves back through history. ^N moves forward through history. ^R starts a backward-search. #\begin{tabular}{|cl|} \hline #\multicolumn{2}{|c|}{Command-line Editing Commands} \\ \hline \hline #Character & Function \\ \hline # & \multicolumn{1}{|c|}{Line Editing}\\ \cline{2-2} #\verb~^B~ & move back a single character.\\ #\verb~^F~ & move forward a single character.\\ #\verb~^A~ & move to the beginning of the line.\\ #\verb~^E~ & move to the end of the line.\\ #\verb~^H~ & delete the previous character.\\ #\verb~DEL~ & delete the current character.\\ #\verb~^D~ & delete current character. EOF if line is empty.\\ #\verb~^K~ & delete from current position to the end of line.\\ #\verb~^L~ & redraw line in case it gets trashed.\\ #\verb~^U~ & delete the entire line. \\ #\verb~^W~ & delete previous word. \\ #\verb~^V~ & inhibits the interpretation of the following key as editing command. \\ #\verb~TAB~ & performs filename-completion. \\ \hline # & \multicolumn{1}{|c|}{History} \\ \cline{2-2} #\verb~^P~ & move back through history.\\ #\verb~^N~ & move forward through history.\\ #\verb~^R~ & starts a backward-search.\\ %c l . %Character@Function %_ %@Line Editing %^B@move back a single character. %^F@move forward a single character. %^A@move to the beginning of the line. %^E@move to the end of the line. %^H@delete the previous character. %DEL@delete the current character. %^D@delete current character. EOF if line is empty. %^K@delete from current position to the end of line. %^L@redraw line in case it gets trashed. %^U@delete the entire line. %^W@delete previous word. %_ %^V@inhibits the interpretation of the following key as editing command. %TAB@performs filename-completion. %_ %@History %^P@move back through history. %^N@move forward through history. %^R@starts a backward-search. @end table ^ ^^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^

Character	Function
	Line Editing
`^B`	move back a single character.
`^F`	move forward a single character.
`^A`	move to the beginning of the line.
`^E`	move to the end of the line.
`^H`	delete the previous character.
`DEL`	delete the current character.
`^D`	delete current character. EOF if line is empty
`^K`	delete from current position to the end of line.
`^L`	redraw line in case it gets trashed.
`^U`	delete the entire line.
`^W`	delete previous word.
`^V`	inhibits the interpretation of the following key as editing command.
`TAB`	performs filename-completion.
	History
`^P`	move back through history.
`^N`	move forward through history.
`^R`	starts a backward-search.

2 Comments ?comments The comment character `#` may appear almost anywhere in a command line, and `gnuplot` will ignore the rest of that line. A `#` does not have this effect inside a quoted string. Note that if a commented line ends in '\' then the subsequent line is also treated as part of the comment. See also `set datafile commentschars` for specifying a comment character for data files. 2 Coordinates ?coordinates =axes The commands `set arrow`, `set key`, `set label` and `set object` allow you to draw something at an arbitrary position on the graph. This position is specified by the syntax: {} , {} {,{} } Each can either be `first`, `second`, `polar`, `graph`, `screen`, or `character`. `first` places the x, y, or z coordinate in the system defined by the left and bottom axes; `second` places it in the system defined by the x2,y2 axes (top and right); `graph` specifies the area within the axes---0,0 is bottom left and 1,1 is top right (for splot, 0,0,0 is bottom left of plotting area; use negative z to get to the base---see `set xyplane`); `screen` specifies the screen area (the entire area---not just the portion selected by `set size`), with 0,0 at bottom left and 1,1 at top right. `character` coordinates are used primarily for offsets, not absolute positions. The `character` vertical and horizontal size depend on the current font. `polar` causes the first two values to be interpreted as angle theta and radius r rather than as x and y. This could be used, for example, to place labels on a 2D plot in polar coordinates or a 3D plot in cylindrical coordinates. If the coordinate system for x is not specified, `first` is used. If the system for y is not specified, the one used for x is adopted. In some cases, the given coordinate is not an absolute position but a relative value (e.g., the second position in `set arrow` ... `rto`). In most cases, the given value serves as difference to the first position. If the given coordinate belongs to a log-scaled axis, a relative value is interpreted as multiplier. For example, set logscale x set arrow 100,5 rto 10,2 plots an arrow from position 100,5 to position 1000,7 since the x axis is logarithmic while the y axis is linear. If one (or more) axis is timeseries, the appropriate coordinate should be given as a quoted time string according to the `timefmt` format string. See `set xdata` and `set timefmt`. `Gnuplot` will also accept an integer expression, which will be interpreted as seconds relative to 1 January 1970. 2 Datastrings ?datastrings Data files may contain string data consisting of either an arbitrary string of printable characters containing no whitespace or an arbitrary string of characters, possibly including whitespace, delimited by double quotes. The following line from a datafile is interpreted to contain four columns, with a text field in column 3: 1.000 2.000 "Third column is all of this text" 4.00 Text fields can be positioned within a 2-D or 3-D plot using the commands: plot 'datafile' using 1:2:4 with labels splot 'datafile' using 1:2:3:4 with labels A column of text data can also be used to label the ticmarks along one or more of the plot axes. The example below plots a line through a series of points with (X,Y) coordinates taken from columns 3 and 4 of the input datafile. However, rather than generating regularly spaced tics along the x axis labeled numerically, gnuplot will position a tic mark along the x axis at the X coordinate of each point and label the tic mark with text taken from column 1 of the input datafile. set xtics plot 'datafile' using 3:4:xticlabels(1) with linespoints =columnheader There is also an option that will interpret the first entry in a column of input data (i.e. the column heading) as a text field, and use it as the key title for data plotted from that column. The example given below will use the first entry in column 2 to generate a title in the key box, while processing the remainder of columns 2 and 4 to draw the required line: plot 'datafile' using 1:(f($2)/$4) with lines title columnhead(2) Another example: plot for [i=2:6] 'datafile' using i title "Results for ".columnhead(i) This use of column headings is automated by `set datafile columnheaders` or `set key autotitle columnhead`. See `labels`, `using xticlabels`, `plot title`, `using`, `key autotitle`. 2 Enhanced text mode ?enhanced text ?enhanced ?text_markup ?markup ?bold ?italic Many terminal types support an enhanced text mode in which additional formatting information can be embedded in the text string. For example, "x^2" will write x-squared as we are used to seeing it, with a superscript 2. This mode is selected by default when you set the terminal, but may be toggled afterward using "set termoption [no]enhanced", or disabled for individual strings as in `set label "x_2" noenhanced`. Note: For output to TeX-based terminals (e.g. cairolatex, pict2e, pslatex, tikz) all text strings should instead use TeX/LaTeX syntax. See `latex`. @start table - first is interactive cleartext form Control Examples Explanation ^ a^x superscript _ a_x subscript @ @x or a@^b_{cd} phantom box (occupies no width) & &{space} inserts space of specified length ~ ~a{.8-} overprints '-' on 'a', raised by .8 times the current fontsize {/Times abc} print abc in font Times at current size {/Times*2 abc} print abc in font Times at twice current size {/Times:Italic abc} print abc in font Times with style italic {/Arial:Bold=20 abc} print abc in boldface Arial font size 20 \U+ \U+221E Unicode point U+221E (INFINITY) #\begin{tabular}{|clll|} \hline #\multicolumn{4}{|c|}{Enhanced Text Control Codes} \\ \hline #Control & Example & Result & Explanation \\ \hline #\verb~^~ & \verb~a^x~ & $a^x$ & superscript\\ #\verb~_~ & \verb~a_x~ & $a_x$ & subscript\\ #\verb~@~ & \verb~a@^b_{cd}~ & $a^b_{cd}$ &phantom box (occupies no width)\\ #\verb~&~ & \verb~d&{space}b~ & d\verb*+ +b & inserts space of specified length\\ #\verb|~| & \verb|~a{.8-}| & $\tilde{a}$ & overprints '-' on 'a', raised by .8\\ #\verb~ ~ & \verb~ ~ & ~ ~ & times the current fontsize\\ #\verb| | & \verb|{/Times abc}| & {\rm abc} & print abc in font Times at current size\\ #\verb| | & \verb|{/Times*2 abc}| & \Large{\rm abc} & print abc in font Times at twice current size\\ #\verb| | & \verb|{/Times:Italic abc}| & {\it abc} & print abc in font Times with style italic\\ #\verb| | & \verb|{/Arial:Bold=20 abc}| & \Large\textsf{\textbf{abc}} & print abc in boldface Arial font size 20\\ #\verb|\U+| & \verb|\U+221E| & $\infty$ & Unicode point U+221E INFINITY\\ %c c l . C ugly - doc2ms uses @ for column separator, but here we C need @ in table, so end and restart the table ! %.TE %.TS %center box tab ($) ; %c c l . %Control$Examples$Explanation %_ %^$a^x$superscript %\&_$a\&_x$subscript % @ $ @x or a\&@^b\&_{cd}$phantom box (occupies no width) % & $ &{space}$inserts space of specified length % ~ $ ~a{.8-}$overprints '-' on 'a', raised by .8 % $ $times the current fontsize @end table ^ ^^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^

Control	Examples	Explanation
`^`	`a^x`	superscript
`_`	`a_x`	subscript
`@`	`@x` or `a@^b_{cd}`	phantom box (occupies no width)
`&`	`&{space}`	inserts space of specified length
`~`	`~a{.8-}`	overprints '-' on 'a', raised by .8 times the current fontsize

The markup control characters act on the following single character or bracketed clause. The bracketed clause may contain a string of characters with no additional markup, e.g. 2^{10}, or it may contain additional markup that changes font properties. Font specifiers MUST be preceded by a '/' character that immediately follows the opening '{'. If a font name contains spaces it must be enclosed in single or double quotes. Examples: The first example illustrates nesting one bracketed clause inside another to produce a boldface A with an italic subscript i, all in the current font. If the clause introduced by :Normal were omitted the subscript would be both italic and boldface. The second example illustrates the same markup applied to font "Times New Roman" at 20 point size. {/:Bold A_{/:Normal{/:Italic i}}} {/"Times New Roman":Bold=20 A_{/:Normal{/:Italic i}}} The phantom box is useful for a@^b_c to align superscripts and subscripts but does not work well for overwriting a diacritical mark on a letter. For that purpose it is much better to use an encoding (e.g. utf8) that contains letters with accents or other diacritical marks. See `set encoding`. Since the box is non-spacing, it is sensible to put the shorter of the subscript or superscript in the box (that is, after the @). Space equal in length to a string can be inserted using the '&' character. Thus 'abc&{def}ghi' would produce 'abc ghi'. The '~' character causes the next character or bracketed text to be overprinted by the following character or bracketed text. The second text will be horizontally centered on the first. Thus '~a/' will result in an 'a' with a slash through it. You can also shift the second text vertically by preceding the second text with a number, which will define the fraction of the current fontsize by which the text will be raised or lowered. In this case the number and text must be enclosed in brackets because more than one character is necessary. If the overprinted text begins with a number, put a space between the vertical offset and the text ('~{abc}{.5 000}'); otherwise no space is needed ('~{abc}{.5---}'). You can change the font for one or both strings ('~a{.5 /*.2 o}'---an 'a' with a one-fifth-size 'o' on top---and the space between the number and the slash is necessary), but you can't change it after the beginning of the string. Neither can you use any other special syntax within either string. Control characters must be escaped, e.g. '~a{.8\^}' to print Ã¢. See `escape sequences` below. Note that strings in double-quotes are parsed differently than those enclosed in single-quotes. The major difference is that backslashes may need to be doubled when in double-quoted strings. The file "ps_guide.ps" in the /docs/psdoc subdirectory of the gnuplot source distribution contains more examples of the enhanced syntax, as does the demo ^ `enhanced_utf8.dem` ^ 3 escape sequences ?escape sequences ?enhanced text escape sequences ?unicode The backslash character \ is used to escape single byte character codes or Unicode entry points. The form \ooo (where ooo is a 3 character octal value) can be used to index a known character code in a specific font encoding. For example the Adobe Symbol font uses a custom encoding in which octal 245 represents the infinity symbol. You could embed this in an enhanced text string by giving the font name and the character code "{/Symbol \245}". This is mostly useful for the PostScript terminal, which cannot easily handle UTF-8 encoding. You can specify a character by its Unicode code point as \U+hhhh, where hhhh is the 4 or 5 character hexadecimal code point. For example the code point for the infinity symbol âˆž is \U+221E. This will be converted to a UTF-8 byte sequence on output if appropriate. In a UTF-8 environment this mechanism is not needed for printable special characters since they are handled in a text string like any other character. However it is useful for combining forms or supplemental diacritical marks (e.g. an arrow over a letter to represent a vector). See `set encoding`, `utf8`, and the ^ online unicode demo. ^ 2 Environment ?environment A number of shell environment variables are understood by `gnuplot`. None of these are required. GNUTERM, if defined, is passed to "set term" on start-up. This can be overridden by a system or personal initialization file (see `startup`) and of course by later explicit `set term` commands. Terminal options may be included. E.g. bash$ export GNUTERM="postscript eps color size 5in, 3in" GNUHELP, if defined, sets the pathname of the HELP file (gnuplot.gih). Initialization at start-up may search for configuration files $HOME/.gnuplot, and $XDG_CONFIG_HOME/gnuplot/gnuplotrc. On MS-DOS, Windows and OS/2, files in GNUPLOT or USERPROFILE are searched. For more details see `startup`. On Unix, PAGER is used as an output filter for help messages. On Unix, SHELL is used for the `shell` command. On MS-DOS and OS/2, COMSPEC is used. FIT_SCRIPT may be used to specify a `gnuplot` command to be executed when a fit is interrupted---see `fit`. FIT_LOG specifies the default filename of the logfile maintained by fit. GNUPLOT_LIB may be used to define additional search directories for data and command files. The variable may contain a single directory name, or a list of directories separated by a platform-specific path separator, eg. ':' on Unix, or ';' on DOS/Windows/OS/2 platforms. The contents of GNUPLOT_LIB are appended to the `loadpath` variable, but not saved with the `save` and `save set` commands. Several gnuplot terminal drivers access TrueType fonts via the gd library (see `fonts`). For these terminals GDFONTPATH and GNUPLOT_DEFAULT_GDFONT may affect font selection. The postscript terminal uses its own font search path. It is controlled by the environmental variable GNUPLOT_FONTPATH. GNUPLOT_PS_DIR is used by the postscript driver to search for external prologue files. Depending on the build process, gnuplot contains either a built-in copy of those files or a default hardcoded path. You can use this variable to have the postscript terminal use custom prologue files rather than the default prologue files. See `postscript prologue`. 2 Expressions ?expressions ?division In general, any mathematical expression accepted by C, FORTRAN, Pascal, or BASIC is valid. The precedence of these operators is determined by the specifications of the C programming language. White space (spaces and tabs) is ignored inside expressions. Note that gnuplot uses both "real" and "integer" arithmetic, like FORTRAN and C. Integers are entered as "1", "-10", etc; reals as "1.0", "-10.0", "1e1", 3.5e-1, etc. The most important difference between the two forms is in division: division of integers truncates: 5/2 = 2; division of reals does not: 5.0/2.0 = 2.5. In mixed expressions, integers are "promoted" to reals before evaluation: 5/2e0 = 2.5. The result of division of a negative integer by a positive one may vary among compilers. Try a test like "print -5/2" to determine if your system always rounds down (-5/2 yields -3) or always rounds toward zero (-5/2 yields -2). The integer expression "1/0" may be used to generate an "undefined" flag, which causes a point to be ignored. Or you can use the pre-defined variable NaN to achieve the same result. See `using` for an example. =NaN Gnuplot can also perform simple operations on strings and string variables. For example, the expression ("A" . "B" eq "AB") evaluates as true, illustrating the string concatenation operator and the string equality operator. A string which contains a numerical value is promoted to the corresponding integer or real value if used in a numerical expression. Thus ("3" + "4" == 7) and (6.78 == "6.78") both evaluate to true. An integer, but not a real or complex value, is promoted to a string if used in string concatenation. A typical case is the use of integers to construct file names or other strings; e.g. ("file" . 4 eq "file4") is true. Substrings can be specified using a postfixed range descriptor [beg:end]. For example, "ABCDEF"[3:4] == "CD" and "ABCDEF"[4:*] == "DEF" The syntax "string"[beg:end] is exactly equivalent to calling the built-in string-valued function substr("string",beg,end), except that you cannot omit either beg or end from the function call. 3 Complex values ?complex values ?complex Arithmetic operations and most built-in functions support the use of complex arguments. Complex constants are expressed as {,}, where and must be numerical constants. Thus {0,1} represents 'i'. The program predefines a variable I = {0,1} on entry that can be used to generate complex values in terms of other variables. Thus `x + y*I` is a valid expression but `{x,y}` is not. The real and imaginary components of complex value z can be extracted as real(z) and imag(z). The modulus is given by abs(z). The phase angle is given by arg(z). Ffigure_E0 Gnuplot's 2D and 3D plot styles expect real values; to plot a complex-valued function f(z) with non-zero imaginary components you must plot the real or imaginary component, or the modulus or phase. For example to represent the modulus and phase of a function f(z) with complex argument and complex result it is possible to use the height of the surface to represent modulus and use the color to represent the phase. It is convenient to use a color palette in HSV space with component H (hue), running from 0 to 1, mapped to the range of the phase returned by arg(z), [-Ï€:Ï€], so that the color wraps when the phase angle does. By default this would be at H = 0 (red). You can change this with the `start` keyword in `set palette` so that some other value of H is mapped to 0. The example shown starts and wraps at H = 0.3 (green). See `set palette defined`, `arg`, `set angles`. set palette model HSV start 0.3 defined (0 0 1 1, 1 1 1 1) set cbrange [-pi:pi] set cbtics ("-Ï€" -pi, "Ï€" pi) set pm3d corners2color c1 E0(z) = exp(-z)/z I = {0,1} splot '++' using 1:2:(abs(E0(x+I*y))):(arg(E0(x+I*y))) with pm3d 3 Constants ?constants ?expressions constants ?octal ?hexadecimal ?complex constants Integer constants are interpreted via the C library routine strtoll(). This means that constants beginning with "0" are interpreted as octal, and constants beginning with "0x" or "0X" are interpreted as hexadecimal. Floating point constants are interpreted via the C library routine atof(). Complex constants are expressed as {,}, where and must be numerical constants. For example, {0,1} represents 'i' itself; {3,2} represents 3 + 2i. The curly braces are explicitly required here. The program predefines a variable I = {0,1} on entry that can be used to avoid typing the explicit form. For example `3 + 2*I` is the same as `{3,2}`, with the advantage that it can be used with variable coefficient for the imaginary component. Thus `x + y*I` is a valid expression but `{x,y}` is not. String constants consist of any sequence of characters enclosed either in single quotes or double quotes. The distinction between single and double quotes is important. See `quotes`. Examples: 1 -10 0xffaabb # integer constants 1.0 -10. 1e1 3.5e-1 # floating point constants {1.2, -3.4} # complex constant "Line 1\nLine 2" # string constant (\n is expanded to newline) '123\na\456' # string constant (\ and n are ordinary characters) #TeX \newpage 3 Functions ?expressions functions Arguments to math functions in `gnuplot` can be integer, real, or complex unless otherwise noted. Functions that accept or return angles (e.g. sin(x)) treat angle values as radians, but this may be changed to degrees using the command `set angles`. ^ ^^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^

Math library and built-in functions
Function	Arguments	Returns
abs(x)	int or real	\|x\|, absolute value of x; same type
abs(x)	complex	length of x, √( Re(x)² + Im(x)² )
acos(x)	any	cos^-1 x (inverse cosine)
acosh(x)	any	cosh^-1 x (inverse hyperbolic cosine)
airy(x)	real	Airy function Ai(x) for real x
arg(x)	complex	the phase of x
asin(x)	any	sin^-1 x (inverse sin)
asinh(x)	any	sinh^-1 x (inverse hyperbolic sin)
atan(x)	any	tan^-1 x (inverse tangent)
atan2(y,x)	int or real	tan^-1(y/x) (inverse tangent)
atanh(x)	any	tanh^-1 x (inverse hyperbolic tangent)
besj0(x)	real	J₀ Bessel function of x in radians
besj1(x)	real	J₁ Bessel function of x in radians
besjn(n,x)	int,real	J_n Bessel function of x in radians
besy0(x)	real	Y₀ Bessel function of x in radians
besy1(x)	real	Y₁ Bessel function of x in radians
besyn(n,x)	int,real	Y_n Bessel function of x in radians
besi0(x)	real	Modified Bessel function of order 0, x in radians
besi1(x)	real	Modified Bessel function of order 1, x in radians
besin(n,x)	int,real	Modified Bessel function of order n, x in radians
cbrt(x)	real	cube root of x, domain and range both real
ceil(x)	any	⌈x⌉, smallest integer not less than x (real part)
conj(x)	complex	complex conjugate of x
cos(x)	radians	cos x, cosine of x
cosh(x)	any	cosh x, hyperbolic cosine of x in radians
EllipticK(k)	real k in (-1:1)	K(k) complete elliptic integral of the first kind
EllipticE(k)	real k in [-1:1]	E(k) complete elliptic integral of the second kind
EllipticPi(n,k)	real n<1, real k in (-1:1)	Π(n,k) complete elliptic integral of the third kind
erf(x)	any	erf(Re(x)), error function of real(x)
erfc(x)	any	erfc(Re(x)), 1.0 - error function of real(x)
exp(x)	any	e^x, exponential function of x
expint(n,x)	any	E_n(x), exponential integral function of x
floor(x)	any	⌊x⌋, largest integer not greater than x (real part)
gamma(x)	any	Γ(Re(x)), gamma function of real(x)
ibeta(p,q,x)	any	ibeta(Re(p,q,x)), ibeta function of real(p,q,x)
inverf(x)	any	inverse error function real(x)
igamma(a,z)	complex	igamma(a>0,z), igamma function of complex a>0,z
imag(x)	complex	Im(x), imaginary part of x as a real number
int(x)	real	integer part of x, truncated toward zero
invibeta(a,b,p)	0<p<1	inverse incomplete beta function
invigamma(a,p)	0<p<1	inverse incomplete gamma function
invnorm(x)	any	inverse normal distribution function real(x)
LambertW(z,k)	complex, int	kth branch of complex Lambert W function
lambertw(x)	real	principal branch (k=0) of Lambert W function
lgamma(x)	real	lgamma(Re(x)), lgamma function of real(x)
lnGamma(x)	complex	lnGamma(x) valid over entire complex plane
log(x)	any	ln x, natural logarithm (base e) of x
log10(x)	any	log₁₀ x, logarithm (base 10) of x
norm(x)	any	norm(x), normal distribution function of real(x)
rand(x)	int	pseudo random number in the interval (0:1)
real(x)	any	Re(x), real part of x
sgn(x)	any	1 if x > 0, -1 if x < 0, 0 if x = 0. ℑ(x) ignored
Sign(x)	complex	0 if x = 0, otherwise x/\|x\|
sin(x)	any	sin x, sine of x
sinh(x)	any	sinh x, hyperbolic sine of x in radians
sqrt(x)	any	√x, square root of x
SynchrotronF(x)	real	Synchtrotron function F
tan(x)	any	tan x, tangent of x
tanh(x)	any	tanh x, hyperbolic tangent of x in radians
uigamma(a,x)	real	uigamma(a,x), upper incomplete gamma function a>0,x
voigt(x,y)	real	convolution of Gaussian and Lorentzian
zeta(s)	any	Riemann zeta function

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Special functions from libcerf (only if available)
Function	Arguments	Returns
cerf(z)	complex	complex error function
cdawson(z)	complex	complex Dawson's integral
faddeeva(z)	complex	rescaled complex error function w(z) = exp(-zÂ²) Ã— erfc(-iz)
erfi(x)	real	imaginary error function erfi(x) = -i Ã— erf(ix)
FresnelC(x)	real	cosine (real) component of Fresnel integral
FresnelS(x)	real	sine (imaginary) component of Fresnel integral
VP(x,sigma,gamma)	real	Voigt profile
VP_fwhm(sigma,gamma)	real	Voigt profile full width at half max

^ ^^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^

String functions
Function	Arguments	Returns
gprintf("format",x,...)	any	string result from applying gnuplot's format parser
sprintf("format",x,...)	multiple	string result from C-language sprintf
strlen("string")	string	number of characters in string
strstrt("string","key")	strings	int index of first character of substring "key"
substr("string",beg,end)	multiple	string "string"[beg:end]
split("string","separator")	string	array containing individual fields of original string
join(array,"separator")	array,string	concatenates array elements into a string
strftime("timeformat",t)	any	string result from applying gnuplot's time parser
strptime("timeformat",s)	string	seconds since year 1970 as given in string s
system("command")	string	string containing output stream of shell command
trim(" string ")	string	string without leading or trailing whitespace
word("string",n)	string, int	returns the nth word in "string"
words("string")	string	returns the number of words in "string"

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time functions
Function	Arguments	Returns
time(x)	any	the current system time
timecolumn(N,format)	int, string	formatted time data from column N of input data
tm_hour(t)	time in sec	the hour
tm_mday(t)	time in sec	the day of the month
tm_min(t)	time in sec	the minute
tm_mon(t)	time in sec	the month
tm_sec(t)	time in sec	the second
tm_wday(t)	time in sec	the day of the week
tm_week(t)	time in sec	ISO 8601 week of year
tm_yday(t)	time in sec	the day of the year
tm_year(t)	time in sec	the year
weekdate_iso(year,week,day)	int	time eqv to ISO 8601 standard week date
weekdate_cdc(year,week,day)	int	time eqv to CDC epidemiological week date

^ ^^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^

other gnuplot functions
Function	Arguments	Returns
column(x)	int or string	contents of column x during data input.
columnhead(x)	int	string containing first entry of column x in datafile.
exists("X")	string	returns 1 if a variable named X is defined, 0 otherwise.
hsv2rgb(h,s,v)	h,s,v in [0:1]	converts HSV color to 24bit RGB color.
index(A,x)	array, any	returns i such that A[i] equals x
palette(z)	real	24bit RGB palette color mapped to z
rgbcolor("name")	string	32bit ARGB color from name
stringcolumn(x)	int	content column x as a string.
valid(x)	int	test validity of column x during datafile input
value("name")	string	returns the current value of the named variable.

C For TeX and troff output a table replaces the help sections below. C For the HTML help we want both, table and sections, so the magic C marker below is used to signal this to doc2html: ^ @start table #\begin{longtable}{@{\extracolsep{\fill}}|lcrl|@{}} \hline #\multicolumn{4}{|c|}{Math library and built-in functions} \\ \hline \hline #Function & Arguments & ~ & Returns ({\gpCX } indicates complex result) \\ \hline #\endhead \hline \endfoot %c c l . %Function@Arguments@Returns %_ 4 abs ?expressions functions abs ?abs #abs(x) & int or real & ~ & absolute value of $x$, $|x|$ \\ #abs(x) & complex & ~ & length of $x$, $\sqrt{{\mbox{real}(x)^{2} + #\mbox{imag}(x)^{2}}}$ \\ %abs(x)@int or real@absolute value of $x$, $|x|$ %abs(x)@complex@length of $x$, $sqrt{roman real (x) sup 2 + roman imag (x) sup 2}$ The `abs(x)` function returns the absolute value of its argument. The returned value is of the same type as the argument. =norm =modulus For complex arguments, abs(x) is defined as the length of x in the complex plane [i.e., sqrt(real(x)**2 + imag(x)**2) ]. This is also known as the norm or complex modulus of x. 4 acos ?expressions functions acos ?acos #acos(x) & ~~ & \gpCX & $\cos^{-1} x$ (inverse cosine) \\ %acos(x)@ ~~ @$cos sup -1 x$ (inverse cosine) The `acos(x)` function returns the arc cosine (inverse cosine) of its argument. `acos` returns its argument in radians or degrees, as selected by `set angles`. 4 acosh ?expressions functions acosh ?acosh #acosh(x) & ~~ & \gpCX & $\cosh^{-1} x$ (inverse hyperbolic cosine) \\ %acosh(x)@ ~~ @$cosh sup -1 x$ (inverse hyperbolic cosine) The `acosh(x)` function returns the inverse hyperbolic cosine of its argument in radians or degrees, as selected by `set angles`. 4 airy ?expressions functions airy ?airy #airy(x) & real & ~ & Airy function Ai(x) for real x\\ %airy(x)@ real @Airy function Ai(x) for real x The `airy(x)` function returns the value of the Airy function Ai(x) of its argument. The function Ai(x) is that solution of the equation y'' - x y = 0 which is everywhere finite. If the argument is complex, its imaginary part is ignored. 4 arg ?expressions functions arg ?arg #arg(x) & complex & ~ & the phase of $x$, $-\pi\leq$arg($x$)$\leq\pi$ \\ %arg(x)@complex@the phase of $x$ The `arg(x)` function returns the phase of a complex number in radians or degrees, as selected by `set angles`. 4 asin ?expressions functions asin ?asin #asin(x) & ~~ & \gpCX & $\sin^{-1} x$ (inverse sin) \\ %asin(x)@ ~~ @$sin sup -1 x$ (inverse sin) The `asin(x)` function returns the arc sin (inverse sin) of its argument. `asin` returns its argument in radians or degrees, as selected by `set angles`. 4 asinh ?expressions functions asinh ?asinh #asinh(x) & ~~ & \gpCX & $\sinh^{-1} x$ (inverse hyperbolic sin) \\ %asinh(x)@ ~~ @$sinh sup -1 x$ (inverse hyperbolic sin) The `asinh(x)` function returns the inverse hyperbolic sin of its argument in radians or degrees, as selected by `set angles`. 4 atan ?expressions functions atan ?atan #atan(x) & ~~ & \gpCX & $\tan^{-1} x$ (inverse tangent) \\ %atan(x)@ ~~ @$tan sup -1 x$ (inverse tangent) The `atan(x)` function returns the arc tangent (inverse tangent) of its argument. `atan` returns its argument in radians or degrees, as selected by `set angles`. 4 atan2 ?expressions functions atan2 ?atan2 #atan2(y,x) & int or real & ~ & $\tan^{-1} (y/x)$ (inverse tangent) \\ %atan2(y,x)@int or real@$tan sup -1 (y/x)$ (inverse tangent) The `atan2(y,x)` function returns the arc tangent (inverse tangent) of the ratio of the real parts of its arguments. `atan2` returns its argument in radians or degrees, as selected by `set angles`, in the correct quadrant. 4 atanh ?expressions functions atanh ?atanh #atanh(x) & ~~ & \gpCX & $\tanh^{-1} x$ (inverse hyperbolic tangent) \\ %atanh(x)@ ~~ @$tanh sup -1 x$ (inverse hyperbolic tangent) The `atanh(x)` function returns the inverse hyperbolic tangent of its argument in radians or degrees, as selected by `set angles`. 4 besj0 ?expressions functions besj0 ?besj0 # besj0(x) & real & ~ & $J_{0}$ Bessel function of $x$ in radians \\ %besj0(x)@real@$J sub 0$ Bessel function of $x$ in radians The `besj0(x)` function returns the J0th Bessel function of its argument. `besj0` expects its argument to be in radians. 4 besj1 ?expressions functions besj1 ?besj1 # besj1(x) & real & ~ & $J_{1}$ Bessel function of $x$ in radians \\ %besj1(x)@real@$J sub 1$ Bessel function of $x$ in radians The `besj1(x)` function returns the J1st Bessel function of its argument. `besj1` expects its argument to be in radians. 4 besjn ?expressions functions besjn ?besjn # besjn(n,x) & int, real & ~ & $J_{n}$ Bessel function of $x$ in radians \\ %besjn(n,x)@int,real@$J sub n$ Bessel function of $x$ in radians The `besjn(n,x)` functions returns the Jn Bessel function of x in radians. 4 besy0 ?expressions functions besy0 ?besy0 # besy0(x) & real & ~ & $Y_{0}$ Bessel function of $x$ in radians \\ %besy0(x)@real@$Y sub 0$ Bessel function of $x$ in radians The `besy0(x)` function returns the Y0th Bessel function of its argument. `besy0` expects its argument to be in radians. 4 besy1 ?expressions functions besy1 ?besy1 # besy1(x) & real & ~ & $Y_{1}$ Bessel function of $x$ in radians \\ %besy1(x)@real@$Y sub 1$ Bessel function of $x$ in radians The `besy1(x)` function returns the Y1st Bessel function of its argument. `besy1` expects its argument to be in radians. 4 besyn ?expressions functions besyn ?besyn # besyn(n,x) & int, real & ~ & $Y_{n}$ Bessel function of $x$ in radians \\ %besyn(n,x)@int,real@$Y sub n$ Bessel function of $x$ in radians The `besyn(n,x)` functions returns the Yn Bessel function of x in radians. 4 besi0 ?expressions functions besi0 ?besi0 # besi0(x) &real & ~ & Modified Bessel function of order 0, $x$ in radians \\ %besi0(x)@real@ Modified Bessel function of order 0, $x$ in radians The `besi0(x)` function is the modified Bessel function or order 0. `besi0` expects its argument to be in radians. 4 besi1 ?expressions functions besi1 ?besi1 # besi1(x) &real & ~ & Modified Bessel function of order 1, $x$ in radians \\ %besi1(x)@real@ Modified Bessel function of order 1, $x$ in radians The `besi1(x)` function is the modified Bessel function or order 1. `besi1` expects its argument to be in radians. 4 besin ?expressions functions besin ?besin # besin(n,x) &int, real & ~ & Modified Bessel function of order n, $x$ in radians \\ %besin(x)@int,real@ Modified Bessel function of order n, $x$ in radians `besin(n,x)` is the modified Bessel function or order n for integer n and x in radians. 4 cbrt ?expressions functions cbrt ?cbrt #cbrt(x) & real & ~ & cube root of $x$ (domain and range both limited to real) \\ %cbrt(x)@ real @ cube root of x (domain and range both limited to real) `cbrt(x)` returns the cube root of x. If x is not real, returns NaN. ?? C 4 ceil C ?expressions functions ceil #ceil(x) & ~~ & ~ & $\lceil x \rceil$, smallest integer not less than the real part of $x$ \\ %ceil(x)@ ~~ @$left ceiling x right ceiling$, smallest integer not less than $x$ (real part) `ceil(x)` returns the smallest integer not less than the real part of x. Outside the domain |x|<2^52 ceil(x) returns NaN. 4 conj ?expressions functions conj ?conj #conj(x) & complex & \gpCX & complex conjugate of $x$ \\ %conj(x)@complex@complex conjugate of $x$ The `conj(x)` function returns the complex conjugate x. conj( {r, i} ) = {r, -i} 4 cos ?expressions functions cos ?cos #cos(x) & ~~ & \gpCX & $\cos x$, cosine of $x$ \\ %cos(x)@radians@$cos~x$, cosine of $x$ The `cos(x)` function returns the cosine of its argument. `cos` accepts its argument in radians or degrees, as selected by `set angles`. 4 cosh ?expressions functions cosh ?cosh #cosh(x) & ~~ & \gpCX & $\cosh x$, hyperbolic cosine of $x$ in radians \\ %cosh(x)@ ~~ @$cosh~x$, hyperbolic cosine of $x$ in radians The `cosh(x)` function returns the hyperbolic cosine of its argument. `cosh` expects its argument to be in radians. ?expressions functions EllipticK ?EllipticK 4 EllipticK #EllipticK(k) & real k $\in$ (-1:1) & ~ & $K(k)$ complete elliptic integral of the first kind \\ %EllipticK(k)@real k in (-1:1)@$K ( k )$ complete elliptic integral of the first kind The `EllipticK(k)` function returns the complete elliptic integral of the first kind. See `elliptic integrals` for more details. ?expressions functions EllipticE ?EllipticE 4 EllipticE #EllipticE(k) & real k $\in$ [-1:1] & ~ & $E(k)$ complete elliptic integral of the second kind \\ %EllipticE(k)@real k in [-1:1]@ $E ( k )$ complete elliptic integral of the second kind The `EllipticE(k)` function returns the complete elliptic integral of the second kind. See `elliptic integrals` for more details. ?expressions functions EllipticPi ?EllipticPi 4 EllipticPi #EllipticPi(n,k) & real n$<$1, real k $\in$ (-1:1) & ~ & $\Pi(n,k)$ complete elliptic integral of the third kind \\ %EllipticPi(n,k)@ real n<1, real k in (-1:1)@ $Pi ( n,k )$ complete elliptic integral of the third kind The `EllipticPi(n,k)` function returns the complete elliptic integral of the third kind. See `elliptic integrals` for more details. 4 erf ?expressions functions erf ?erf #erf(x) & ~~ & ~ & $\mbox{erf}(\mbox{real}(x))$, error function of real($x$) \\ %erf(x)@ ~~ @$erf ( roman real (x))$, error function of real ($x$) The `erf(x)` function returns the error function of the real part of its argument. If the argument is a complex value, the imaginary component is ignored. See `cerf`, `erfc`, `inverf`, and `norm`. 4 erfc ?expressions functions erfc ?erfc #erfc(x) & ~~ & ~ & $\mbox{erfc}(\mbox{real}(x))$, 1.0 - error function of real($x$) \\ %erfc(x)@ ~~ @$erfc ( roman real (x))$, 1.0 - error function of real ($x$) The `erfc(x)` function returns 1.0 - the error function of the real part of its argument. If the argument is a complex value, the imaginary component is ignored. See `cerf`, `erf`, `inverf`, and `norm`. 4 exp ?expressions functions exp ?exp #exp(x) & ~~ & \gpCX & $e^{x}$, exponential function of $x$ \\ %exp(x)@ ~~ @$e sup x$, exponential function of $x$ The `exp(x)` function returns `e` raised to the power of x, which can be an integer, real, or complex value. ?? C 4 expint #expint(n,x) & int $n\ge0$, real $x\ge0$ & ~ & $E_n(x)=\int_1^\infty t^{-n} e^{-xt}\,dt$, exponential integral of $x$ \\ %expint(n,x)@ ~~ @$E sub n (x)$, exponential integral function of $x$ ?? C 4 floor C ?expressions functions floor #floor(x) & ~~ & ~ & $\lfloor x \rfloor$, largest integer not greater #than the real part of $x$ \\ %floor(x)@ ~~ @$left floor x right floor$, largest integer not greater than $x$ (real part) `floor(x)` returns the largest integer not greater than the real part of x. Outside the domain |x|<2^52 floor(x) returns NaN. 4 gamma ?expressions functions gamma #gamma(x) & ~~ & ~ & $\Gamma(x)$, gamma function of real($x$) \\ %gamma(x)@ ~~ @$GAMMA ( roman real (x))$, gamma function of real ($x$) The `gamma(x)` function returns the gamma function of the real part of its argument. For integer n, gamma(n+1) = n!. If the argument is a complex value, the imaginary component is ignored. For complex arguments see `lnGamma`. ?? C 4 ibeta #ibeta(a,b,x) & $a,b>0$, $x \in [0:1]$ & ~ & $B(a,b,x)=\frac{\Gamma(a+b)}{\Gamma(a)\Gamma(b)}\intop_{0}^{x}t^{a-1}(1-t)^{b-1}dt$, incomplete beta \\ %ibeta(a,b,x)@ ~~ @$ibeta ( roman real (a,b,x))$, ibeta function of real ($a$,$b$,$x$) 4 inverf ?expressions functions inverf ?inverf #inverf(x) & ~~ & ~ & inverse error function of real($x$) \\ %inverf(x)@ ~~ @inverse error function real($x$) The `inverf(x)` function returns the inverse error function of the real part of its argument. See `erf` and `invnorm`. ?? C 4 igamma #igamma(a,z) & complex, $\Re(a)>0$ & \gpCX & incomplete gamma function $P(a,z)=\frac{1}{\Gamma(z)}\intop_{0}^{z}t^{a-1}e^{-t}dt$ \\ %igamma(a,z)@ ~~ @$igamma (a,z)$, lower incomplete gamma function of ($a$,$z$) 4 imag ?expressions functions imag ?imag #imag(x) & complex & ~ & imaginary part of $x$ as a real number \\ %imag(x)@complex@imaginary part of $x$ as a real number The `imag(x)` function returns the imaginary part of its argument as a real number. ?? C 4 int C ?expressions functions int #int(x) & real & ~ & integer part of $x$, truncated toward zero \\ %int(x)@real@integer part of $x$, truncated toward zero int(x) returns the integer part of its argument, truncated toward zero. 4 invnorm ?expressions functions invnorm ?invnorm #invnorm(x) & ~~ & ~ & inverse normal distribution function of real($x$) \\ %invnorm(x)@ ~~ @inverse normal distribution function real($x$) The `invnorm(x)` function returns the inverse cumulative normal (Gaussian) distribution function of the real part of its argument. See `norm`. ?? C 4 invibeta #invibeta(a,b,p) & real & ~ & inverse incomplete beta function \\ %invibeta(a,b,p)@ real @inverse incomplete beta function ?? C 4 invigamma #invigamma(a,p) & real & ~ & inverse incomplete gamma function \\ %invigamma(a,p)@ real @inverse incomplete gamma function #LambertW(z,k) & complex, int & \gpCX & kth branch of complex Lambert W function \\ %LambertW(z,k) & complex, int & $k$th branch of complex Lambert W function 4 lambertw ?expressions functions lambertw ?lambertw #lambertw(x) & real & ~ & principal branch (k=0) of Lambert W function \\ %lambertw(x)@real@principal branch (k=0) of Lambert W function The `lambertw(x)` function returns the value of the principal branch (k=0) of Lambert's W function, which is defined by the equation (W(x)*exp(W(x))=x. x must be a real number with x >= -exp(-1). 4 lgamma ?expressions functions lgamma ?lgamma #lgamma(x) & real & ~ & $\ln\Gamma(x)$ for real $x$ \\ %lgamma(x)@real@lgamma function of real $x$ The `lgamma(x)` function returns the natural logarithm of the gamma function of the real part of its argument. If the argument is a complex value, the imaginary component is ignored. For complex values use lnGamma(z). 4 lngamma #lnGamma(x) & complex & \gpCX & $\ln\Gamma(x)$ valid over entire complex plane \\ %lnGamma(x)@complex@lgamma function valid over entire complex plane The `lnGamma(x)` function returns the natural logarithm of the gamma function. This implementation uses a Lanczos approximation valid over the entire complex plane. The imaginary component of the result is phase-shifted to yield a continuous surface everywhere except the negative real axis. 4 log ?expressions functions log ?log #log(x) & ~~ & \gpCX & $\log_{e} x$, natural logarithm (base $e$) of $x$ \\ %log(x)@ ~~ @$ln~x$, natural logarithm (base $e$) of $x$ The `log(x)` function returns the natural logarithm (base `e`) of its argument. See `log10`. 4 log10 ?expressions functions log10 ?log10 #log10(x) & ~~ & \gpCX & $\log_{10} x$, logarithm (base $10$) of $x$ \\ %log10(x)@ ~~ @${log sub 10}~x$, logarithm (base $10$) of $x$ The `log10(x)` function returns the logarithm (base 10) of its argument. 4 norm ?expressions functions norm ?norm #norm(x) & ~~ & ~ & normal distribution (Gaussian) function of real($x$) \\ %norm(x)@ ~~ @$norm(x)$, normal distribution function of real($x$) The `norm(x)` function returns the cumulative normal (Gaussian) distribution function of the real part of its argument. See `invnorm`, `erf` and `erfc`. 4 rand ?expressions functions rand ?rand #rand(x) & int & ~ & pseudo random number in the open interval (0:1) \\ %rand(x)@int@pseudo random number in the open interval (0:1) The `rand(x)` function returns a pseudo random number in the interval (0:1). See `random` for more details. 4 real ?expressions functions real ?real #real(x) & ~~ & ~ & real part of $x$ \\ %real(x)@ ~~ @real part of $x$ The `real(x)` function returns the real part of its argument. ?? C 4 round C ?expressions functions round #round(x) & ~~ & ~ & $\lfloor x \rceil$, integer nearest to the real part of $x$ \\ %round(x)@ ~~ @ integer nearest to the real part of $x$ `round(x)` returns the integer nearest to the real part of x. Outside the domain |x|<2^52 round(x) returns NaN. 4 sgn ?expressions functions sgn ?sgn #sgn(x) & ~~ & ~ & 1 if $x>0$, -1 if $x<0$, 0 if $x=0$. imag($x$) ignored \\ %sgn(x)@ ~~ @1 if $x > 0$, -1 if $x < 0$, 0 if $x = 0$. $roman imag (x)$ ignored The `sgn(x)` function returns 1 if its argument is positive, -1 if its argument is negative, and 0 if its argument is 0. If the argument is a complex value, the imaginary component is ignored. 4 Sign #Sign(x) & complex & \gpCX & 0 if $x = 0$, otherwise $x/|x|$ \\ %Sign(x)@complex@0 if $x = 0$, otherwise $x/|x|$ The `Sign(x)` function returns 0 if its argument is zero, otherwise it returns the complex value Sign(x) = x/|x|. 4 sin ?expressions functions sin ?sin #sin(x) & ~~ & \gpCX & $\sin x$, sine of $x$ \\ %sin(x)@ ~~ @$sin~x$, sine of $x$ The `sin(x)` function returns the sine of its argument. `sin` expects its argument to be in radians or degrees, as selected by `set angles`. 4 sinh ?expressions functions sinh ?sinh #sinh(x) & ~~ & \gpCX & $\sinh x$, hyperbolic sine of $x$ in radians \\ %sinh(x)@ ~~ @$sinh~x$, hyperbolic sine of $x$ in radians The `sinh(x)` function returns the hyperbolic sine of its argument. `sinh` expects its argument to be in radians. 4 sqrt ?expressions functions sqrt ?sqrt #sqrt(x) & ~~ & \gpCX & $\sqrt{x}$, square root of $x$ \\ %sqrt(x)@ ~~ @$sqrt x $, square root of $x$ The `sqrt(x)` function returns the square root of its argument. If the x is a complex value, this always returns the root with positive real part. ?? C 4 SynchrotronF C ?expressions functions SynchrotronF #SynchrotronF(x) & real & ~ & $F(x) = x\intop_{x}^{\infty}K_{\frac{5}{3}}(\nu)~d\nu$ \\ %SynchrotronF(x)@ ~~ @ Synchrotron function F% 4 tan ?expressions functions tan ?tan #tan(x) & ~~ & \gpCX & $\tan x$, tangent of $x$ \\ %tan(x)@ ~~ @$tan~x$, tangent of $x$ The `tan(x)` function returns the tangent of its argument. `tan` expects its argument to be in radians or degrees, as selected by `set angles`. 4 tanh ?expressions functions tanh ?tanh #tanh(x) & ~~ & \gpCX & $\tanh x$, hyperbolic tangent of $x$ in radians\\ %tanh(x)@ ~~ @$tanh~x$, hyperbolic tangent of $x$ in radians The `tanh(x)` function returns the hyperbolic tangent of its argument. `tanh` expects its argument to be in radians. ?? C 4 uigamma #uigamma(a,x) & real, real & & upper incomplete gamma function $Q(a,x)=\frac{1}{\Gamma(x)}\intop_{x}^{\infty}t^{a-1}e^{-t}dt$ \\ %uigamma(a,x)@ ~~ @$uigamma (a,x)$, upper incomplete gamma function of ($a$,$x$) 4 voigt ?expressions functions voigt ?voigt #voigt(x,y) & real & ~ & Voigt/Faddeeva function $\frac{y}{\pi} \int{\frac{exp(-t^2)}{(x-t)^2+y^2}}dt$ \\ # & & ~ & Note: voigt$(x,y)$ = $real($faddeeva$(x+iy))$ \\ %voigt(x,y)@real@convolution of Gaussian and Lorentzian The function `voigt(x,y)` returns an approximation to the Voigt/Faddeeva function used in spectral analysis. The approximation is accurate to one part in 10^4. If the libcerf library is available, the re_w_of_z() routine is used to provide a more accurate value. Note that voigt(x,y) = real(faddeeva( x + y*{0,1} )). ?? C 4 zeta #zeta(s) & complex & \gpCX & Riemann zeta function $\zeta(s) = \Sigma^{\infty}_{k=1} k^{-s}$\\ %zeta(s)@complex@Riemann zeta function #\hline \end{longtable} #%% begin dummy tabular because the @end processing wants to end one #\begin{tabular}{|lcl|} @end table ^ @start table #\setlength\LTleft{0pt} #\setlength\LTright{0pt} #\begin{longtable}{@{\extracolsep{\fill}}|lcrl|@{}} \hline #\multicolumn{4}{|c|}{Special functions from libcerf (only if available)} \\ \hline \hline #Function ~~~~~~~~~~~~~~~~~ & Arguments & ~ & Returns ({\gpCX } indicates complex result)\\ \hline #\endhead \hline \endfoot %c c l . %Function@Arguments@Returns %_ # ~ & ~ & ~ & \hspace{9cm} \\ 4 cerf ?expressions functions cerf ?cerf #cerf(z) & complex & \gpCX & complex error function $cerf(z)={\frac{\sqrt{\pi}}{2}}{\int^{z}_{0}{e^{-t^2}dt}} $ \\ %cerf(z)@complex@complex error function `cerf(z)` is the complex version of the error function erf(x) Requires external library libcerf. 4 cdawson ?expressions functions cdawson ?cdawson =Dawson's integral ?Dawson's integral %cdawson(z)@complex@complex Dawson's integral #cdawson(z)&complex& \gpCX &complex extension of Dawson's integral $D(z)={\frac{\sqrt{\pi}}{2}e^{-z^2} erfi(z)} $ \\ `cdawson(z)` returns Dawson's Integral evaluated for the complex argument z. cdawson(z) = sqrt(pi)/2 * exp(-z^2) * erfi(z) Requires external library libcerf. 4 faddeeva ?expressions functions faddeeva ?faddeeva %faddeeva(z)@complex@scaled complex complementary error function w(z) = exp(-z^2) * erfc(-i*z) #faddeeva(z)&complex& \gpCX &scaled complex complementary error function $w(z) = e^{-z^2}~ erfc(-iz) $ \\ `faddeeva(z)` returns the scaled complex complementary error function faddeeva(z) = exp(-z^2) * erfc(-i*z) This corresponds to Eqs 7.1.3 and 7.1.4 of Abramowitz and Stegun. Requires external library libcerf. 4 erfi ?expressions functions erfi ?erfi %erfi(x)@real@imaginary error function erfi(x) = -i * erf(ix) #erfi(x)&real&~&imaginary error function $erf(x) = -i * erf(ix)$ \\ Imaginary error function erfi(x) = -i * erf(ix) Requires external library libcerf. ?? C 4 FresnelC %FresnelC(x)@real@ C(x) = integral[0;x] cos(pi/2 t^2)dt #FresnelC(x)&real&~&Fresnel integral $C(x)=\int^{x}_{0}\cos(\frac{\pi}{2}t^2)dt$ \\ ?? C 4 FresnelS %FresnelS(x)@real@ S(x) = integral[0;x] sin(pi/2 t^2)dt #FresnelS(x)&real&~&Fresnel integral $S(x)=\int^{x}_{0}\sin(\frac{\pi}{2}t^2)dt$ \\ 4 Voigt Profile ?expressions functions VP ?expressions functions VP_fwhm ?VP ?VP_fwhm %VP(x,sigma,gamma)@real@Voigt profile %VP_fwhm(sigma,gamma)@real@Voigt profile full width at half maximum #VP(x,$\sigma$,$\gamma$)&real& ~ & Voigt profile $ VP(x,\sigma,\gamma) = {\int^{\infty}_{-\infty}{G(x^\prime;\sigma) L(x-x^\prime;\gamma) dx^\prime }} $ \\ #VP\_fwhm($\sigma$,$\gamma$)&real& ~ & Voigt profile full width at half maximum value\\ `VP(x,sigma,gamma)` corresponds to the Voigt profile defined by convolution of a Gaussian G(x;sigma) with a Lorentzian L(x;gamma). `VP_fwhm(sigma,gamma)` gives the full width at half maximum value of this function. #\hline \end{longtable} #%% begin dummy tabular because the @end processing wants to end one #\begin{tabular}{|lcl|} @end table ^ @start table #\setlength\LTleft{0pt} #\setlength\LTright{0pt} #\begin{longtable}{@{\extracolsep{\fill}}|lcrl|@{}} \hline #\multicolumn{4}{|c|}{Complex special functions from Amos library (only if available)} \\ \hline \hline #Function ~~~~~~~~~~~~~~~~~ & Arguments & ~ & Returns ({\gpCX } indicates complex result)\\ \hline #\endhead \hline \endfoot %c c l . %Function@Arguments@Returns %_ # ~ & ~ & ~ & \hspace{9cm} \\ #Ai(z) & complex & \gpCX & complex Airy function $Ai(z)$\\ %Ai(z)@complex@complex Airy function $Ai(z)$ #Bi(z) & complex & \gpCX & complex Airy function $Bi(z)$\\ %Bi(z)@complex@complex Airy function $Bi(z)$ #BesselH1(nu,z) & real, complex & \gpCX & $H^{(1)}_{\nu}(z)$ Hankel function of the first kind\\ %BesselH1(nu,z) @ real, complex @ Hankel function H1_nu of the first kind #BesselH2(nu,z) & real, complex & \gpCX & $H^{(2)}_{\nu}(z)$ Hankel function of the second kind\\ %BesselH2(nu,z) @ real, complex @ Hankel function H2_nu of the second kind #BesselJ(nu,z) & real, complex & \gpCX & $J_{\nu}(z)$ Bessel function of the first kind\\ %BesselJ(nu,z) @ real, complex @ Bessel function J_nu of the first kind #BesselY(nu,z) & real, complex & \gpCX & $Y_{\nu}(z)$ Bessel function of the second kind\\ %BesselY(nu,z) @ real, complex @ Bessel function Y_nu of the second kind #BesselI(nu,z) & real, complex & \gpCX & $I_{\nu}(z)$ modified Bessel function of the first kind\\ %BesselI(nu,z) @ real, complex @ modified Bessel function I_nu of the first kind #BesselK(nu,z) & real, complex & \gpCX & $K_{\nu}(z)$ modified Bessel function of the second kind\\ %BesselK(nu,z) @ real, complex @ modified Bessel function K_nu of the second kind #expint(n,z) & int $n\geq0$, complex $z$ & \gpCX & $E_n(z)=\int_1^\infty t^{-n} e^{-zt}\,dt$, exponential integral\\ %expint(n,z)@ int n>=0, complex @$E sub n (z)$, complex exponential integral function #\hline \end{longtable} #%% begin dummy tabular because the @end processing wants to end one #\begin{tabular}{|lcl|} @end table ^ @start table #\begin{longtable}{@{\extracolsep{\fill}}|lcl|@{}} \hline #\multicolumn{3}{|c|}{String functions} \\ \hline \hline #Function & Arguments & Returns \\ \hline %c c l . %Function@Arguments@Returns %_ 4 gprintf ?expressions functions gprintf #gprintf("format",x,...) & any & string result from applying gnuplot's format parser \\ %gprintf("format",x,...)@any@string result from applying gnuplot's format parser `gprintf("format",x)` applies gnuplot's own format specifiers to the single variable x and returns the resulting string. If you want standard C-language format specifiers, you must instead use `sprintf("format",x)`. See `format specifiers`. 4 sprintf ?expressions functions sprintf ?sprintf #sprintf("format",x,...) & multiple & string result from C-language sprintf \\ %sprintf("format",x,...)@multiple@string result from C-language sprintf `sprintf("format",var1,var2,...)` applies standard C-language format specifiers to multiple arguments and returns the resulting string. If you want to use gnuplot's own format specifiers, you must instead call `gprintf()`. For information on sprintf format specifiers, please see standard C-language documentation or the unix sprintf man page. 4 strlen ?expressions functions strlen ?strlen #strlen("string") & string & number of characters in string\\ %strlen("string")@string@number of characters in string `strlen("string")` returns the number of characters in a string taking into account the current encoding. If the current encoding supports multibyte characters (SJIS UTF8), this may be less than the number of bytes in the string. If the string contains multibyte UTF8 characters but the current encoding is set to something other than UTF8, strlen("utf8string") will return a value that is larger than the actual number of characters. 4 strstrt ?expressions functions strstrt ?strstrt #strstrt("string","key") & strings & int index of first character of substring "key" \\ %strstrt("string","key")@strings@int index of first character of substring "key" `strstrt("string","key")` searches for the character string "key" in "string" and returns the index to the first character of "key". If "key" is not found, it returns 0. Similar to C library function strstr except that it returns an index rather than a string pointer. strstrt("hayneedlestack","needle") = 4. This function is aware of utf8 encoding, so strstrt("Î±Î²Î³","Î²") returns 2. 4 substr ?expressions functions substr ?substr =substring #substr("string",beg,end) & multiple & string "string"[beg:end] \\ %substr("string",beg,end)@multiple@string "string"[beg:end] `substr("string",beg,end)` returns the substring consisting of characters beg through end of the original string. This is exactly equivalent to the expression "string"[beg:end] except that you do not have the option of omitting beg or end. 4 split ? #split("string","sep") & string & array of substrings \\ %split("string","sep")@string@array of substrings `split("string", "sep")` uses the character sequence in "sep" as a field separator to split the content of "string" into individual fields. It returns an array of strings, each corresponding to one field of the original string. The second parameter "sep" is optional. If "sep" is omitted or if it contains a single space character the fields are split by any amount of whitespace (space, tab, formfeed, newline, return). Otherwise the full sequence of characters in "sep" must be matched. For examples, see `counting_words`. 4 join ? `join(array, "sep")` concatenates the string elements of an array into a single string containing fields delimited by the character sequence in "sep". Non-string array elements generate an empty field. For examples, see `counting_words`. #join(array,"sep") & array,string & concatenate array elements into a string\\ %join(array,"sep") @array,string@concatenate array elements into a string 4 strftime ?expressions functions strftime ?strftime #strftime("timeformat",t) & any & string result from applying gnuplot's time parser \\ %strftime("timeformat",t)@any@string result from applying gnuplot's time parser `strftime("timeformat",t)` applies the timeformat specifiers to the time t given in seconds since the year 1970. See `time_specifiers` and `strptime`. 4 strptime ?expressions functions strptime ?strptime #strptime("timeformat",s) & string & seconds since year 1970 as given in string s \\ %strptime("timeformat",s)@string@seconds since year 1970 as given in string s `strptime("timeformat",s)` reads the time from the string s using the timeformat specifiers and converts it into seconds since the year 1970. See `time_specifiers` and `strftime`. 4 system ?expressions functions system =system #system("command") & string & string containing output stream of shell command \\ %system("command")@string@string containing output stream of shell command `system("command")` executes "command" using the standard shell and returns the resulting character stream from stdout as string variable. One optional trailing newline is ignored. This can be used to import external functions into gnuplot scripts using 'f(x) = real(system(sprintf("somecommand %f", x)))'. 4 trim =trim ?expressions functions trim #trim(" string ") & string & string without leading or trailing whitespace \\ %trim(" string ")@string@string without leading or trailing whitespace `trim(" padded string ")` returns the original string stripped of leading and trailing whitespace. This is useful for string comparisons of input data fields that may contain extra whitespace. For example plot FOO using 1:( trim(strcol(3)) eq "A" ? $2 : NaN ) 4 word ? =word #word("string",n) & string, int & returns the nth word in "string" \\ %word("string",n)@string, int@returns the nth word in "string" `word("string",n)` returns the nth word in string. For example, `word("one two three",2)` returns the string "two". 4 words =words #words("string") & string & returns the number of words in "string" \\ %words("string")@string@returns the number of words in "string" `words("string")` returns the number of words in string. For example, `words(" a b c d")` returns 4. #\hline \end{longtable} #%% begin dummy tabular because the @end processing wants to end one #\begin{tabular}{|lcl|} @end table ^ @start table #\begin{tabular}{|lcl|} \hline #\multicolumn{3}{|c|}{Time functions} \\ \hline \hline #Function & Arguments & Returns \\ \hline %c c l . %Function@Arguments@Returns %_ ?? C 4 time C ?expressions functions time #time(x) & any & the current system time in seconds \\ %time(x)@any@the current system time in seconds ?? C 4 timecolumn C ?expressions functions timecolumn #timecolumn(N,"timeformat") & int, string & formatted time data from column $N$ of input \\ %timecolumn(N,"timeformat")@int, string@formatted time data from column $N$ of input ?? C 4 tm_hour ?expressions functions tm_hour ?tm_hour #tm\_hour(t) & time in sec & the hour (0..23)\\ %tm_hour(t)@time in sec@the hour (0..23) The `tm_hour(t)` function interprets its argument as a time, in seconds from 1 Jan 1970. It returns the hour (an integer in the range 0--23) as a real. ?? C 4 tm_mday ?expressions functions tm_mday ?tm_mday #tm\_mday(t) & time in sec & the day of the month (1..31)\\ %tm_mday(t)@time in sec@the day of the month (1..31) The `tm_mday(t)` function interprets its argument as a time, in seconds from 1 Jan 1970. It returns the day of the month (an integer in the range 1--31) as a real. ?? C 4 tm_min ?expressions functions tm_min ?tm_min #tm\_min(t) & time in sec & the minute (0..59)\\ %tm_min(t)@time in sec@the minute (0..59) The `tm_min(t)` function interprets its argument as a time, in seconds from 1 Jan 1970. It returns the minute (an integer in the range 0--59) as a real. ?? C 4 tm_mon ?expressions functions tm_mon ?tm_mon #tm\_mon(t) & time in sec & the month (0..11)\\ %tm_mon(t)@time in sec@the month (0..11) The `tm_mon(t)` function interprets its argument as a time, in seconds from 1 Jan 1970. It returns the month (an integer in the range 0--11) as a real. ?? C 4 tm_sec ?expressions functions tm_sec ?tm_sec #tm\_sec(t) & time in sec & the second (0..59)\\ %tm_sec(t)@time in sec@the second (0..59) The `tm_sec(t)` function interprets its argument as a time, in seconds from 1 Jan 1970. It returns the second (an integer in the range 0--59) as a real. ?? C 4 tm_wday ?expressions functions tm_wday ?tm_wday #tm\_wday(t) & time in sec & the day of the week (Sun..Sat) as (0..6)\\ %tm_wday(t)@time in sec@the day of the week (Sun..Sat) as (0..6) The `tm_wday(t)` function interprets its argument as a time, in seconds from 1 Jan 1970. It returns the day of the week (Sun..Sat) as an integer (0..6). ?? C 4 tm_week #tm\_week(t) & time in sec & week of year in ISO8601 "week date" system (1..53)\\ %tm_week(t)@time in sec@ISO 8601 week of year in ISO8601 "week date" system (1..53) ?? C 4 tm_yday ?expressions functions tm_yday ?tm_yday #tm\_yday(t) & time in sec & the day of the year (0..365)\\ %tm_yday(t)@time in sec@the day of the year (0..365) The `tm_yday(t)` function interprets its argument as a time, in seconds from 1 Jan 1970. It returns the day of the year (an integer in the range 0--365) as a real. ?? C 4 tm_year ?expressions functions tm_year ?tm_year #tm\_year(t) & time in sec & the year \\ %tm_year(t)@time in sec@the year The `tm_year(t)` function interprets its argument as a time, in seconds from 1 Jan 1970. It returns the year (an integer) as a real. ?? C 4 weekdata_iso #weekdate\_iso(year,week,day) & int & time corresponding to ISO 8601 standard week date\\ %weekdate_iso(year,week,day)@int@ time corresponding to ISO 8601 standard week date ?? C 4 weekdata_cdc #weekdate\_cdc(year,week,day) & int & time corresponding to CDC epidemiological week date\\ %weekdate_cdc(year,week,day)@int@ time corresponding to CDC epidemiological week date @end table ^ @start table #\begin{tabular}{|lcl|} \hline #\multicolumn{3}{|c|}{other {\bf gnuplot} functions} \\ \hline \hline #Function & Arguments & Returns \\ \hline %c c l . %Function@Arguments@Returns %_ ?? #column(x) & int or string & numerical value of column $x$ during datafile input \\ %column(x)@int or string@numerical value of column $x$ during datafile input ?? #columnhead(x) & int & string containing first entry of column $x$ in datafile. \\ %columnhead(x)@int@string containing first entry of column $x$ in datafile. ?? 4 exists ?expressions functions exists ?exists #exists("X") & string & returns 1 if a variable named X is defined, 0 otherwise. \\ %exists("X")@string@returns 1 if a variable named X is defined, 0 otherwise. The argument to `exists()` is a string constant or a string variable; if the string contains the name of a defined variable, the function returns 1. Otherwise the function returns 0. 4 hsv2rgb ?expressions functions hsv2rgb ?hsv2rgb ?hsv #hsv2rgb(h,s,v) & h,s,v $\in$ [0:1] & 24bit RGB color value. \\ %hsv2rgb(h,s,v)@h,s,v in [0:1]@24bit RGB color value. The `hsv2rgb(h,s,v)` function converts HSV (Hue/Saturation/Value) triplet to an equivalent RGB value. ?? #index(A,x) & array, any & integer i such that A[i] = x. 0 if no match.\\ %index(A,x)@array, any@integer i such that A[i] = x. 0 if no match. 4 palette ?expressions functions palette ?palette #palette(z) & real & 24 bit RGB palette color mapped to z. \\ %palette(z)@real@24 bit RGB palette color mapped to z. `palette(z)` returns the 24 bit RGB representation of the palette color mapped to z given the current extremes of cbrange. 4 rgbcolor ?expressions functions rgbcolor ?rgbcolor =alpha channel #rgbcolor("name") & string & 32bit ARGB color from name or string representation. \\ %rgbcolor("name")@string@32bit ARGB color from name or string representation. `rgbcolor("name")` returns an integer containing the 32 bit alpha + RGB color value of a named color or a string of the form "0xAARRGGBB" or "#AARRGGBB". If the string is not recognized as a color description the function returns 0. This can be used to read a color name from a data file or to add an alpha channel to a named color in the upper byte of the returned value. See `colorspec`. ?? #stringcolumn(x) & int or string & content of column $x$ as a string \\ %stringcolumn(x)@int or string@content column $x$ as a string. ?? #valid(x) & int & test validity of column $x$ during datafile input\\ %valid(x)@int@test validity of column $x$ during datafile input. ?? #value("name") & string & returns the value of the named variable.\\ %value("name")@string@returns the current value of the named variable. 4 voxel ?expressions functions voxel ?voxel #voxel(x,y,z) & real & value of the active grid voxel containing point (x,y,z)\\ %voxel(x,y,z)@real@value of the active grid voxel containing point (x,y,z) The function voxel(x,y,z) returns the value of the voxel in the currently active grid that contains the point (x,y,z). It may also be used on the left side of an assignment statement to set the value of that voxel. E.g. voxel(x,y,z) = 0.0 See `splot voxel-grids`, `vgrid`. @end table 4 integer conversion functions (int floor ceil round) ?integer conversion ?integer ?precision Gnuplot integer variables are stored with 64 bits of precision if that is supported by the platform. Gnuplot complex and real variables are on most platforms stored in IEEE754 binary64 (double) floating point representation. Their precision is limited to 53 bits, corresponding to roughly 16 significant digits. Therefore integers with absolute value larger than 2^53 cannot be uniquely represented in a floating point variable. I.e. for large N the operation int(real(N)) may return an integer near but not equal to N. Furthermore, functions that convert from a floating point value to an integer by truncation may not yield the expected value if the operation depends on more than 15 significant digits of precision even if the magnitude is small. For example int(log10(0.1)) returns 0 rather than -1 because the floating point representation is equivalent to -0.999999999999999... See also `overflow`. ?expressions functions int ?int `int(x)` returns the integer part of its argument, truncated toward zero. If |x| > 2^63, i.e. too large to represent as an integer, NaN is returned. If |x| > 2^52 the return value will lie within a range of neighboring integers that cannot be distinguished due to limited floating point precision. See `integer conversion`. ?expressions functions floor ?floor `floor(x)` returns the largest integer not greater than the real part of x. If |x| > 2^52 the true value cannot be uniquely determined; in this case the return value is NaN. See `integer conversion`. ?expressions functions ceil ?ceil `ceil(x)` returns the smallest integer not less than the real part of x. If |x| > 2^52 the true value cannot be uniquely determined; in this case the return value is NaN. See `integer conversion`. ?expressions functions round ?round `round(x)` returns the integer nearest to the real part of x. If |x| > 2^52 the true value cannot be uniquely determined; in this case the return value is NaN. See `integer conversion`. 4 elliptic integrals ?elliptic integrals ?elliptic =elliptic integrals The `EllipticK(k)` function returns the complete elliptic integral of the first kind, i.e. the definite integral between 0 and pi/2 of the function `(1 - k^2*sin^2(Î¸))^(-0.5)`. The domain of `k` is -1 to 1 (exclusive). #TeX \quad\quad EllipticK$(k)=\int_0^{\pi/2} {\sqrt{1-k^2\sin^2\theta}~}^{-1}~d\theta$ The `EllipticE(k)` function returns the complete elliptic integral of the second kind, i.e. the definite integral between 0 and pi/2 of the function `(1 - k^2*sin^2(Î¸))^0.5`. The domain of `k` is -1 to 1 (inclusive). #TeX \quad\quad EllipticE$(k)=\int_0^{\pi/2} {\sqrt{1-k^2\sin^2\theta}}~d\theta$ The `EllipticPi(n,k)` function returns the complete elliptic integral of the third kind, i.e. the definite integral between 0 and pi/2 of the function `(1 - k^2*sin^2(Î¸))^(-0.5) / (1 - n*sin^2(Î¸))`. The parameter `n` must be less than 1, while `k` must lie between -1 and 1 (exclusive). Note that by definition EllipticPi(0,k) == EllipticK(k) for all possible values of `k`. #TeX \quad\quad EllipticPi$(n,k)=\int_0^{\pi/2} {\big[(1-n\sin^2\theta)\sqrt{1-k^2\sin^2\theta}~\big]}^{-1}d\theta$ Elliptic integral algorithm: B.C.Carlson 1995, Numerical Algorithms 10:13-26. 4 Complex Airy functions ?expressions functions Ai ?Ai ?expressions functions Bi ?Bi `Ai(z)` and `Bi(z)` are the Airy functions of complex argument z, computed in terms of the modified Bessel functions K and I. Supported via an external library containing routines by Donald E. Amos, Sandia National Laboratories, SAND85-1018 (1985). #TeX \quad\quad Ai$(z) = \frac{1}{\pi}\sqrt{\frac{z}{3}} K_{\nicefrac{1}{3}}(\zeta)$ #TeX \quad\quad\quad $\zeta = \frac{2}{3}z^{\nicefrac{3}{2}}$ #TeX \quad\quad Bi$(z) = \sqrt{\frac{z}{3}} {\big[I_{\nicefrac{-1}{3}}(\zeta) + I_{\nicefrac{1}{3}}(\zeta)]}$ 4 Complex Bessel functions ?expressions functions BesselJ ?BesselJ `BesselJ(nu,z)` is the Bessel function of the first kind J_nu for real argument nu and complex argument z. Supported via external library containing routines by Donald E. Amos, Sandia National Laboratories, SAND85-1018 (1985). ?expressions functions BesselY ?BesselY `BesselY(nu,z)` is the Bessel function of the second kind Y_nu for real argument nu and complex argument z. Supported via external library containing routines by Donald E. Amos, Sandia National Laboratories, SAND85-1018 (1985). ?expressions functions BesselI ?BesselI `BesselI(nu,z)` is the modified Bessel function of the first kind I_nu for real argument nu and complex argument z. Supported via external library containing routines by Donald E. Amos, Sandia National Laboratories, SAND85-1018 (1985). ?expressions functions BesselK ?BesselK `BesselK(nu,z)` is the modified Bessel function of the second kind K_nu for real argument nu and complex argument z. Supported via external library containing routines by Donald E. Amos, Sandia National Laboratories, SAND85-1018 (1985). ?expressions functions BesselH1 ?expressions functions BesselH2 ?expressions functions Hankel ?BesselH1 ?BesselH2 ?Hankel `BesselH1(nu,z)` and `BesselH2(nu,z)` are the Hankel functions of the first and second kind H1(nu,z) = J(nu,z) + iY(nu,z) H2(nu,z) = J(nu,z) - iY(nu,z) for real argument nu and complex argument z. Supported via external library containing routines by Donald E. Amos, Sandia National Laboratories, SAND85-1018 (1985). 4 Expint ?expressions functions expint ?expint `expint(n,z)` returns the exponential integral of order n, where n is an integer >= 0. This is the integral from 1 to infinity of t^(-n) e^(-tz) dt. #TeX \quad\quad $E_n(x)=\int_1^\infty t^{-n} e^{-xt}\,dt$ If your copy of gnuplot was built with support for complex functions from the Amos library, then for n>0 the evaluation uses Amos routine cexint [Amos 1990 Algorithm 683, ACM Trans Math Software 16:178]. In this case z may be any complex number with -pi < arg(z) <= pi. expint(0,z) is calculated as exp(-z)/z. If Amos library support is not present, z is limited to real values z >= 0. 4 Fresnel integrals FresnelC(x) and FresnelS(x) ?expressions functions FresnelC ?expressions functions FresnelS ?FresnelC ?FresnelS The cosine and sine Fresnel integrals are calculated using their relationship to the complex error function erf(z). Due to dependence on erf(z), these functions are only available if libcerf library support is present. #TeX \quad\quad $C(x) = \int^{x}_{0}\cos(\frac{\pi}{2} t^2)dt$ \quad $S(x) = \int^{x}_{0}\sin(\frac{\pi}{2} t^2)dt$ #TeX \quad\quad $C(x)+iS(x)=\frac{1+i}{2} erf(z)$ where $z = \frac{\sqrt{\pi}}{2}(1-i)x$ 4 Gamma ?gamma `gamma(x)` returns the gamma function of the real part of its argument. For integer n, gamma(n+1) = n!. If the argument is a complex value, the imaginary component is ignored. For complex arguments see `lnGamma`. 4 Igamma ?expressions functions igamma ?igamma `igamma(a, z)` returns the lower incomplete gamma function P(a, z), [Abramowitz and Stegun (6.5.1); NIST DLMF 8.2.4]. If complex function support is present a and z may be complex values; real(a) > 0; For the complementary upper incomplete gamma function, see `uigamma`. #TeX \quad\quad igamma$(a,z)=P(a,z) = z^a\gamma^*(a,z)$ #TeX $=\frac{1}{\Gamma(z)}\intop_{0}^{z}t^{a-1}e^{-t}dt$ One of four algorithms is used depending on a and z. #TeX \\ Case (1) When a is large (>100) and (z-a)/a is small (<0.2) use Gauss-Legendre quadrature with coefficients from Numerical Recipes 3rd Edition section 6.2, Press et al (2007). #TeX \\ Case (2) When z > 1 and z > (a+2) use a continued fraction following Shea (1988) J. Royal Stat. Soc. Series C (Applied Statistics) 37:466-473. #TeX \\ Case (3) When z < 0 and a < 75 and imag(a) == 0 use the series from Abramowitz & Stegun (6.5.29). #TeX \\ Otherwise (Case 4) use Pearson's series expansion. Note that convergence is poor in some regions of the full domain. If the chosen algorithm does not converge to within 1.E-14 the function returns NaN and prints a warning. If no complex function support is present the domain is limited to real arguments a > 0, z >= 0. 4 Invigamma ?expressions functions invigamma ?invigamma The inverse incomplete gamma function `invigamma(a,p)` returns the value z such that p = igamma(a,z). p is limited to (0;1]. a must be a positive real number. The implementation in gnuplot has relative accuracy that ranges from 1.e-16 for a<1 to 5.e-6 for a = 1.e10. Convergence may fail for a < 0.005. 4 Ibeta ?expressions functions ibeta ?ibeta `ibeta(a,b,x)` returns the normalized lower incomplete beta integral of real arguments a,b > 0, x in [0:1]. #TeX \quad\quad ibeta$(a,b,x)=\frac{\Gamma(a+b)}{\Gamma(a)\Gamma(b)}\intop_{0}^{x}t^{a-1}(1-t)^{b-1}dt$ If the arguments are complex, the imaginary components are ignored. The implementation in gnuplot uses code from the Cephes library [Moshier 1989, "Methods and Programs for Mathematical Functions", Prentice-Hall]. 4 Invibeta ?expressions functions invibeta ?invibeta The inverse incomplete beta function `invibeta(a,b,p)` returns the value z such that p = ibeta(a,b,z). a, b are limited to positive real values and p is in the interval [0,1]. Note that as a, b approach zero #TeX ($\lessapprox 0.05$) invibeta() approaches 1.0 and its relative accuracy is limited by floating point precision. 4 LambertW ?expressions functions LambertW ?LambertW Lambert W function with complex domain and range. LambertW( z, k ) returns the kth branch of the function W defined by the equation W(z) * exp(z) = z. The complex value is obtained using Halley's method as described by Corless et al [1996], Adv. Comp. Math 5:329. The nominal precision is 1.E-13 but convergence can be poor very close to discontinuities, e.g. branch points. 4 lnGamma ?expressions functions lnGamma ?lnGamma lnGamma(z) returns the natural log of the gamma function with complex domain and range. Implemented using 14 term approximation following Lanczos [1964], SIAM JNA 1:86-96. The imaginary component of the result is phase-shifted to yield a continuous surface everywhere except the negative real axis. 4 Random number generator ?expressions random ?random =rand The function `rand()` produces a sequence of pseudo-random numbers between 0 and 1 using an algorithm from P. L'Ecuyer and S. Cote, "Implementing a random number package with splitting facilities", ACM Transactions on Mathematical Software, 17:98-111 (1991). rand(0) returns a pseudo random number in the open interval (0:1) generated from the current value of two internal 32-bit seeds. rand(-1) resets both seeds to a standard value. rand(x) for integer 0 < x < 2^31-1 sets both internal seeds to x. rand({x,y}) for integer 0 < x,y < 2^31-1 sets seed1 to x and seed2 to y. 4 Special functions with complex arguments ?expressions functions special ?expressions functions complex ?special_functions ?libcerf ?Amos ?libopenspecfun Some special functions with complex domain are provided through external libraries. If your copy of gnuplot was not configured to link against these libraries then it will support only the real domain or will not provide the function at all. Functions requiring libcerf (http://apps.jcns.fz-juelich.de/libcerf) depend on configuration option `--with-libcerf`. This is the default. See `cerf`, `cdawson`, `faddeeva`, `erfi`, `VP`, and `VP_fwhm`. Complex Airy, Bessel, and Hankel functions of real order nu and complex arguments require a library containing routines implemented by Douglas E. Amos, Sandia National Laboratories, SAND85-1018 (1985). These routines may be found in netlib (http://netlib.sandia.gov) or in libopenspecfun (https://github.com/JuliaLang/openspecfun). The corresponding configuration option is `--with-amos=`. See `Ai`, `Bi`, `BesselJ`, `BesselY`, `BesselI`, `BesselK`, `Hankel`. The complex exponential integral is provided by netlib or libamos but not by libopenspecfun. See `expint`. 4 Synchrotron function ?expressions functions SynchrotronF ?SynchrotronF The synchrotron function SynchrotronF(x) describes the power distribution spectrum of synchrotron radiation as a function of x given in units of the critical photon energy (i.e. critical frequency vc). #TeX \quad\quad $F(x) = x\intop_{x}^{\infty}K_{\nicefrac{5}{3}}(\nu)~d\nu$ #TeX where $K_{\nicefrac{5}{3}}$ is a modified Bessel function of the second kind. Chebyshev coefficients for approximation accurate to 1.E-15 are taken from MacLead (2000) NuclInstMethPhysRes A443:540-545. 4 Time functions 5 time ?expressions functions time ?time The `time(x)` function returns the current system time. This value can be converted to a date string with the `strftime` function, or it can be used in conjunction with `timecolumn` to generate relative time/date plots. The type of the argument determines what is returned. If the argument is an integer, time() returns the current time as an integer, in seconds from the epoch date, 1 Jan 1970. If the argument is real (or complex), the result is real as well. If the argument is a string, it is assumed to be a format and it is passed to `strftime` to provide a formatted time string. See also `time_specifiers` and `timefmt`. 5 timecolumn ?expressions functions timecolumn ?timecolumn `timecolumn(N,"timeformat")` reads string data starting at column N as a time/date value and uses "timeformat" to interpret this as "seconds since the epoch" to millisecond precision. If no format parameter is given, the format defaults to the string from `set timefmt`. This function is valid only in the `using` specification of a plot or stats command. See `plot datafile using`. 5 tm_structure ?epoch Gnuplot stores time internally as a 64-bit floating point value representing seconds since the epoch date 1 Jan 1970. In order to interpret this as a time or date it is converted to or from a POSIX standard structure `struct_tm`. Note that fractional seconds, if any, cannot be retrieved via tm_sec(). The components may be accessed individually using the functions #start #b `tm_hour(t)` integer hour in the range 0--23 #b `tm_mday(t)` integer day of month in the range 1--31 #b `tm_min(t)` integer minute in the range 0--59 #b `tm_mon(t)` integer month of year in the range 0--11 #b `tm_sec(t)` integer second in the range 0--59 #b `tm_wday(t)` integer day of the week in the range 0 (Sunday)--6(Saturday) #b `tm_yday(t)` integer day of the year the range 0--365 #b `tm_year(t)` integer year #end 5 tm_week ?expressions functions tm_week ?time_specifiers tm_week ?tm_week ?epidemiological week =epidemiological week The `tm_week(t, standard)` function interprets its first argument t as a time in seconds from 1 Jan 1970. Despite the name of this function it does not report a field from the POSIX tm structure. If standard = 0 it returns the week number in the ISO 8601 "week date" system. This corresponds to gnuplot's %W time format. If standard = 1 it returns the CDC epidemiological week number ("epi week"). This corresponds to gnuplot's %U time format. For corresponding inverse functions that convert week dates to calendar time see `weekdate_iso`, `weekdate_cdc`. In brief, ISO Week 1 of year YYYY begins on the Monday closest to 1 Jan YYYY. This may place it in the previous calendar year. For example Tue 30 Dec 2008 has ISO week date 2009-W01-2 (2nd day of week 1 of 2009). Up to three days at the start of January may come before the Monday of ISO week 1; these days are assigned to the final week of the previous calendar year. E.g. Fri 1 Jan 2021 has ISO week date 2020-W53-5. The US Center for Disease Control (CDC) epidemiological week is a similar week date convention that differs from the ISO standard by defining a week as starting on Sunday, rather than on Monday. 5 weekdate_iso ?expressions functions weekdate_iso ?time_specifiers weekdate_iso ?weekdate_iso Syntax: time = weekdate_iso( year, week [, day] ) This function converts from the year, week, day components of a date in ISO 8601 "week date" format to the calendar date as a time in seconds since the epoch date 1 Jan 1970. Note that the nominal year in the week date system is not necessarily the same as the calendar year. The week is an integer from 1 to 53. The day parameter is optional. If it is omitted or equal to 0 the time returned is the start of the week. Otherwise day is an integer from 1 (Monday) to 7 (Sunday). See `tm_week` for additional information on an inverse function that converts from calendar date to week number in the ISO standard convention. Example: # Plot data from a file with column 1 containing ISO weeks # Week cases deaths # 2020-05 432 1 calendar_date(w) = weekdate_iso( int(w[1:4]), int(w[6:7]) ) set xtics time format "%b\n%Y" plot FILE using (calendar_date(strcol(1))) : 2 title columnhead 5 weekdate_cdc ?expressions functions weekdate_cdc ?time_specifiers weekdate_cdc ?weekdate_cdc =epidemiological week Syntax: time = weekdate_cdc( year, week [, day] ) This function converts from the year, week, day components of a date in the CDC/MMWR "epi week" format to the calendar date as a time in seconds since the epoch date 1 Jan 1970. The CDC week date convention differs from the ISO week date in that it is defined in terms of each week running from day 1 = Sunday to day 7 = Saturday. If the third parameter is 0 or is omitted, the time returned is the start of the week. See `tm_week` and `weekdate_iso`. 4 uigamma ?expressions functions uigamma ?uigamma `uigamma(a, x)` returns the regularized upper incomplete gamma function Q(a, x), NIST DLMF eq 8.2.4 For the complementary lower incomplete gamma function P(a,x), see `igamma`. #TeX \\ Q(a, x) + P(a, x) = 1. #TeX \quad\quad uigamma$(a,z)=Q(a,x) = 1-P(a,x)$ #TeX $=\frac{1}{\Gamma(z)}\intop_{x}^{\infty}t^{a-1}e^{-t}dt$ The current implementation is from the Cephes library (Moshier 2000). The domain is restricted to real a>0, real x>=0. EXPERIMENTAL: To be replaced by an implementation that handles complex arguments. ?? 4 using specifier functions These functions are valid only in the context of data input. Usually this means use in an expression that provides an input field of the `using` specifier in a `plot`, `splot`, `fit`, or `stats` command. However the scope of the functions is actually the full clause of the plot command, including for example use of `columnhead` in constructing the plot title. 5 column ?expressions functions column ?column The `column(x)` function may be used only in the `using` specifier of a plot, splot, fit, or stats command. It evaluates to the numerical value of the content of column x. If the column is expected to hold a string, use instead stringcolumn(x) or timecolumn(x, "timeformat"). See `plot datafile using`, `stringcolumn`, `timecolumn`. 5 columnhead ?expressions functions columnhead ?columnhead The `columnhead(x)` function may only be used as part of a plot, splot, or stats command. It evaluates to a string containing the content of column x in the first line of a data file. This is typically used to extract the column header for use in a plot title. See `plot datafile using`. Example: set datafile columnheader plot for [i=2:4] DATA using 1:i title columnhead(i) 5 stringcolumn ?expressions functions stringcolumn ?stringcolumn ?expressions functions strcol ?strcol The `stringcolumn(x)` function may be used only in the `using` specification of a data plot or `fit` command. It returns the content of column x as a string. `strcol(x)` is shorthand for `stringcolumn(x)`. If the string is to be interpreted as a time or date, use instead timecolumn(x, "timeformat"). See `plot datafile using`. 5 valid ?expressions functions valid ?valid The `valid(x)` function may be used only in expressions that are part of a `using` specification. It can be used to detect explicit NaN values or unexpected garbage in a field of the input stream, perhaps to substitute a default value or to prevent further arithmetic operations using NaN. Both "missing" and NaN (not-a-number) data values are considered to be invalid, but it is important to note that if the program recognizes that a field is truly missing or contains a "missing" flag then the input line is discarded before the expression invoking valid() would be called. See `plot datafile using`, `missing`. Example: # Treat an unrecognized bin value as contributing some constant # prior expectation to the bin total rather than ignoring it. plot DATA using 1 : (valid(2) ? $2 : prior) smooth unique 4 value ?expressions functions value ?value B = value("A") is effectively the same as B = A, where A is the name of a user-defined variable. This is useful when the name of the variable is itself held in a string variable. See `user-defined variables`. It also allows you to read the name of a variable from a data file. If the argument is a numerical expression, value() returns the value of that expression. If the argument is a string that does not correspond to a currently defined variable, value() returns NaN. 4 Counting and extracting words ?counting_words ?expressions functions word ?expressions functions words ?words ?word `word("string",n)` returns the nth word in string. For example, `word("one two three",2)` returns the string "two". `words("string")` returns the number of words in string. For example, `words(" a b c d")` returns 4. The `word` and `words` functions provide limited support for quoted strings, both single and double quotes can be used: print words("\"double quotes\" or 'single quotes'") # 3 A starting quote must either be preceded by a white space, or start the string. This means that apostrophes in the middle or at the end of words are considered as parts of the respective word: print words("Alexis' phone doesn't work") # 4 Escaping quote characters is not supported. If you want to keep certain quotes, the respective section must be surrounded by the other kind of quotes: s = "Keep \"'single quotes'\" or '\"double quotes\"'" print word(s, 2) # 'single quotes' print word(s, 4) # "double quotes" Note, that in this last example the escaped quotes are necessary only for the string definition. =split ?split ?expressions functions split `split("string", "sep")` uses the character sequence in "sep" as a field separator to split the content of "string" into individual fields. It returns an array of strings, each corresponding to one field of the original string. The second parameter "sep" is optional. If "sep" is omitted or if it contains a single space character the fields are split by any amount of whitespace (space, tab, formfeed, newline, return). Otherwise the full sequence of characters in "sep" must be matched. The three examples below each produce an array [ "A", "B", "C", "D" ] t1 = split( "A B C D" ) t2 = split( "A B C D", " ") t3 = split( "A;B;C;D", ";") However the command t4 = split( "A;B; C;D", "; " ) produces an array containing only two strings [ "A;B", "C;D" ] because the two-character field separator sequence "; " is found only once. Note: Breaking the string into an array of single characters using an empty string for sep is not currently implemneted. You can instead accomplish this using single character substrings: Array[i] = "string"[i:i] =join ?join ?expressions functions join `join(array, "sep")` concatenates the string elements of an array into a single string containing fields delimited by the character sequence in "sep". Non-string array elements generate an empty field. The complementary operation `split` break extracts fields from a string to create an array. Example: array A = ["A", "B", , 7, "E"] print join(A,";") A;B;;;E =trim ?trim `trim(" padded string ")` returns the original string stripped of leading and trailing whitespace. This is useful for string comparisons of input data fields that may contain extra whitespace. For example plot FOO using 1:( trim(strcol(3)) eq "A" ? $2 : NaN ) 4 zeta ?expressions functions zeta ?zeta ?Riemann zeta(s) is the Riemann zeta function with complex domain and range. #TeX \quad\quad $\zeta(s) = \Sigma^{\infty}_{k=1}k^{-s}$ This implementation uses the polynomial series described in algorithm 3 of P. Borwein [2000] Canadian Mathematical Society Conference Proceedings. The nominal precision is 1.e-16 over the complex plane. However note that this does not guarantee that non-trivial zeros of the zeta function will evaluate exactly to 0. 3 operators ?expressions operators ?operators The operators in `gnuplot` are the same as the corresponding operators in the C programming language, except that all operators accept integer, real, and complex arguments, unless otherwise noted. The ** operator (exponentiation) is supported, as in FORTRAN. Operator precedence is the same as in Fortran and C. As in those languages, parentheses may be used to change the order of operation. Thus -2**2 = -4, but (-2)**2 = 4. 4 Unary ?expressions operators unary ?operators unary ?unary The following is a list of all the unary operators: @start table - first is interactive cleartext form Symbol Example Explanation - -a unary minus + +a unary plus (no-operation) ~ ~a * one's complement ! !a * logical negation ! a! * factorial $ $3 * data column in `using` specifier || |A| cardinality of array A =factorial =negation =one's complement =operator precedence =cardinality #\begin{tabular}{|lcl|} \hline #\multicolumn{3}{|c|}{Unary Operators}\\ \hline \hline #Symbol & Example & Explanation \\ \hline #\verb@-@ & \verb@-a@ & unary minus \\ #\verb@+@ & \verb@+a@ & unary plus (no-operation) \\ #\verb@~@ & \verb@~a@ & * one's complement \\ #\verb@!@ & \verb@!a@ & * logical negation \\ #\verb@!@ & \verb@a!@ & * factorial \\ #\verb@$@ & \verb@$3@ & * data column in `using` specifier \\ #\verb@|@ & \verb@|A|@ & cardinality of array A \\ C ugly hack: doc2ms uses $ as delimiter for eqn's so it doesn't seem to C be able to print them. So we have to typeset this table without using C eqn (at least that's the only solution I found, without any real docs C on *roff and eqn C First, terminate the table doc2ms.c already started: %c c l . %.TE C ... then turn off eqn delimiters: %.EQ %delim off %.EN C ... and restart the table: %.TS %center box tab (@) ; %c c l . %Symbol@Example@Explanation %_ %-@-a@unary minus %+@+a@unary plus (no-operation) %~@~a@* one's complement %!@!a@* logical negation %!@a!@* factorial %$@$3@* data column in `using` specifier %|@|A|@cardinality of array A @end table ^ ^^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^

Symbol	Example	Explanation
`-`	`-a`	unary minus
`+`	`+a`	unary plus (no-operation)
`~`	`~a`	* one's complement
`!`	`!a`	* logical negation
`!`	`a!`	* factorial
`$`	`$3`	* data column in `using` specifier
`\|`	`\|A\|`	cardinality of array A

Symbol	Example	Explanation
`**`	`a**b`	exponentiation
`*`	`a*b`	multiplication
`/`	`a/b`	division
`%`	`a%b`	* modulo
`+`	`a+b`	addition
`-`	`a-b`	subtraction
`==`	`a==b`	equality
`!=`	`a!=b`	inequality
`<`	`a<b`	less than
`<=`	`a<=b`	less than or equal to
`>`	`a>b`	greater than
`>=`	`a>=b`	greater than or equal to
`<<`	`0xff<<1`	left shift unsigned
`>>`	`0xff>>1`	right shift unsigned
`&`	`a&b`	* bitwise AND
`^`	`a^b`	* bitwise exclusive OR
`\|`	`a\|b`	* bitwise inclusive OR
`&&`	`a&&b`	* logical AND
`\|\|`	`a\|\|b`	* logical OR
`=`	`a = b`	assignment
`,`	`(a,b)`	serial evaluation
`.`	`a.b`	string concatenation
`eq`	`A eq B`	string equality
`ne`	`A ne B`	string inequality

Symbol	Example	Explanation
`?:`	`a?b:c`	* ternary operation

Bit	plot	splot
1	bottom	bottom left front
2	left	bottom left back
4	top	bottom right front
8	right	bottom right back
16	no effect	left vertical
32	no effect	back vertical
64	no effect	right vertical
128	no effect	front vertical
256	no effect	top left back
512	no effect	top right back
1024	no effect	top left front
2048	no effect	top right front
4096	polar	no effect

Format	Explanation
`%f`	floating point notation
`%e` or `%E`	exponential notation; an "e" or "E" before the power
`%g` or `%G`	the shorter of `%e` (or `%E`) and `%f`
`%h` or `%H`	`%g` with "x10^{%S}" or "*10^{%S}" instead of "e%S"
`%x` or `%X`	hex
`%o` or `%O`	octal
`%t`	mantissa to base 10
`%l`	mantissa to base of current logscale
`%s`	mantissa to base of current logscale; scientific power
`%T`	power to base 10
`%L`	power to base of current logscale
`%S`	scientific power
`%c`	character replacement for scientific power
`%b`	mantissa of ISO/IEC 80000 notation (ki, Mi, Gi, Ti, Pi, Ei, Zi, Yi)
`%B`	prefix of ISO/IEC 80000 notation (ki, Mi, Gi, Ti, Pi, Ei, Zi, Yi)
`%P`	multiple of π

Date Format	Explanation
`%a`	abbreviated name of day of the week
`%A`	full name of day of the week
`%b` or `%h`	abbreviated name of the month
`%B`	full name of the month
`%d`	day of the month, 01–31
`%D`	shorthand for `%m/%d/%y` (only output)
`%F`	shorthand for `%Y-%m-%d` (only output)
`%k`	hour, 0–23 (one or two digits)
`%H`	hour, 00–23 (always two digits)
`%l`	hour, 1–12 (one or two digits)
`%I`	hour, 01–12 (always two digits)
`%j`	day of the year, 1–366
`%m`	month, 01–12
`%M`	minute, 0–60
`%p`	"am" or "pm"
`%r`	shorthand for `%I:%M:%S %p` (only output)
`%R`	shorthand for `%H:%M` (only output)
`%S`	second, integer 0–60 on output, (double) on input
`%s`	number of seconds since start of year 1970
`%T`	shorthand for `%H:%M:%S` (only output)
`%U`	week of the year (CDC/MMWR "epi week")
`%w`	day of the week, 0–6 (Sunday = 0)
`%W`	week of the year (ISO 8601 week date)
`%y`	year, 0-99 in range 1969-2068
`%Y`	year, 4-digit
`%z`	timezone, [+-]hh:mm
`%Z`	timezone name, ignored string

Time Format	Explanation
`%tD`	+/- days relative to time=0
`%tH`	+/- hours relative to time=0 (does not wrap at 24)
`%tM`	+/- minutes relative to time=0
`%tS`	+/- seconds associated with previous tH or tM field

(*) Starred explanations indicate that the operator requires an integer argument. The factorial operator returns an integer when N! is sufficiently small (N <= 20 for 64-bit integers). It returns a floating point approximation for larger values of N. ?cardinality The cardinality operator |...| returns the number of elements |A| in array A. It returns the number of data lines |$DATA| when applied to datablock $DATA. 4 Binary ?expressions operators binary ?operators binary The following is a list of all the binary operators: @start table - first is interactive cleartext form Symbol Example Explanation ** a**b exponentiation * a*b multiplication / a/b division % a%b * modulo + a+b addition - a-b subtraction == a==b equality != a!=b inequality < a a>b greater than >= a>=b greater than or equal to << 0xff<<1 left shift unsigned >> 0xff>>2 right shift unsigned & a&b * bitwise AND ^ a^b * bitwise exclusive OR | a|b * bitwise inclusive OR && a&&b * logical AND || a||b * logical OR = a = b assignment , (a,b) serial evaluation . A.B string concatenation eq A eq B string equality ne A ne B string inequality =bitwise operators =string operators =modulo =exponentiation #\begin{tabular}{|lcl|} \hline #\multicolumn{3}{|c|}{Binary Operators} \\ \hline \hline #Symbol & Example & Explanation \\ \hline #\verb~**~ & \verb~a**b~ & exponentiation\\ #\verb~*~ & \verb~a*b~ & multiplication\\ #\verb~/~ & \verb~a/b~ & division\\ #\verb~%~ & \verb~a%b~ & * modulo\\ #\verb~+~ & \verb~a+b~ & addition\\ #\verb~-~ & \verb~a-b~ & subtraction\\ #\verb~==~ & \verb~a==b~ & equality\\ #\verb~!=~ & \verb~a!=b~ & inequality\\ #\verb~<~ & \verb~a~ & \verb~a>b~ & greater than\\ #\verb~>=~ & \verb~a>=b~ & greater than or equal to\\ #\verb~<<~ & \verb~0xff<<1~ & left shift unsigned\\ #\verb~>>~ & \verb~0xff>>1~ & right shift unsigned\\ #\verb~&~ & \verb~a&b~ & * bitwise AND\\ #\verb~^~ & \verb~a^b~ & * bitwise exclusive OR\\ #\verb~|~ & \verb~a|b~ & * bitwise inclusive OR\\ #\verb~&&~ & \verb~a&&b~ & * logical AND\\ #\verb~||~ & \verb~a||b~ & * logical OR\\ #\verb~=~ & \verb~a = b~ & assignment\\ #\verb~,~ & \verb~(a,b)~ & serial evaluation\\ #\verb~.~ & \verb~A.B~ & string concatenation\\ #\verb~eq~ & \verb~A eq B~ & string equality\\ #\verb~ne~ & \verb~A ne B~ & string inequality\\ %c c l . %Symbol@Example@Explanation %_ %**@a**b@exponentiation %*@a*b@multiplication %/@a/b@division %%@a%b@* modulo %+@a+b@addition %-@a-b@subtraction %==@a==b@equality %!=@a!=b@inequality %<@a@a>b@greater than %>=@a>=b@greater than or equal to %<<@0xff<<1@left shift unsigned %>>@0xff>>1@right shift unsigned %&@a&b@* bitwise AND %^@a^b@* bitwise exclusive OR %|@a|b@* bitwise inclusive OR %&&@a&&b@* logical AND %||@a||b@* logical OR %\&=@a = b@assignment %,@(a,b)@serial evaluation %[email protected]@string concatenation %eq@A eq B@string equality %ne@A ne B@string inequality @end table ^ ^^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^

Symbol Example Explanation
** a**b exponentiation
* a*b multiplication
/ a/b division
% a%b * modulo
+ a+b addition
- a-b subtraction
== a==b equality
!= a!=b inequality
< a<b less than
<= a<=b less than or equal to
> a>b greater than
>= a>=b greater than or equal to
<< 0xff<<1 left shift unsigned
>> 0xff>>1 right shift unsigned
& a&b * bitwise AND
^ a^b * bitwise exclusive OR
| a|b * bitwise inclusive OR
&& a&&b * logical AND
|| a||b * logical OR
= a = b assignment
, (a,b) serial evaluation
. a.b string concatenation
eq A eq B string equality
ne A ne B string inequality
(*) Starred explanations indicate that the operator requires integer arguments. Capital letters A and B indicate that the operator requires string arguments. Logical AND (&&) and OR (||) short-circuit the way they do in C. That is, the second `&&` operand is not evaluated if the first is false; the second `||` operand is not evaluated if the first is true. Serial evaluation occurs only in parentheses and is guaranteed to proceed in left to right order. The value of the rightmost subexpression is returned. 4 Ternary ?expressions operators ternary ?operators ternary ?ternary There is a single ternary operator: @start table - first is interactive cleartext form Symbol Example Explanation ?: a?b:c ternary operation #\begin{tabular}{|lcl|} \hline #\multicolumn{3}{|c|}{Ternary Operator} \\ \hline \hline #Symbol & Example & Explanation \\ \hline #\verb~?:~ & \verb~a?b:c~ & ternary operation\\ %c c l . %Symbol@Example@Explanation %_ %?:@a?b:c@ternary operation @end table ^ ^^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^

Symbol Example Explanation
?: a?b:c * ternary operation
The ternary operator behaves as it does in C. The first argument (a), which must be an integer, is evaluated. If it is true (non-zero), the second argument (b) is evaluated and returned; otherwise the third argument (c) is evaluated and returned. The ternary operator is very useful both in constructing piecewise functions and in plotting points only when certain conditions are met. Examples: Plot a function that is to equal sin(x) for 0 <= x < 1, 1/x for 1 <= x < 2, and undefined elsewhere: f(x) = 0<=x && x<1 ? sin(x) : 1<=x && x<2 ? 1/x : 1/0 plot f(x) Note that `gnuplot` quietly ignores undefined values when plotting, so the final branch of the function (1/0) will produce no plottable points. Note also that f(x) will be plotted as a continuous function across the discontinuity if a line style is used. To plot it discontinuously, create separate functions for the two pieces. For data in a file, plot the average of the data in columns 2 and 3 against the datum in column 1, but only if the datum in column 4 is non-negative: plot 'file' using 1:( $4<0 ? 1/0 : ($2+$3)/2 ) For an explanation of the `using` syntax, please see `plot datafile using`. 3 summation ?expressions operators summation ?operators summation ?summation A summation expression has the form sum [= : ] is treated as an integer variable that takes on successive integral values from to . For each of these, the current value of is added to a running total whose final value becomes the value of the summation expression. Examples: print sum [i=1:10] i 55. # Equivalent to plot 'data' using 1:($2+$3+$4+$5+$6+...) plot 'data' using 1 : (sum [col=2:MAXCOL] column(col)) It is not necessary that contain the variable . Although and can be specified as variables or expressions, their value cannot be changed dynamically as a side-effect of carrying out the summation. If is less than then the value of the summation is zero. 3 Gnuplot-defined variables ?expressions gnuplot-defined ?gnuplot-defined ?gnuplot-defined variables ?GPVAL ?gpval Gnuplot maintains a number of read-only variables that reflect the current internal state of the program and the most recent plot. These variables begin with the prefix "GPVAL_". Examples include GPVAL_TERM, GPVAL_X_MIN, GPVAL_X_MAX, GPVAL_Y_MIN. Type `show variables all` to display the complete list and current values. Values related to axes parameters (ranges, log base) are values used during the last plot, not those currently `set`. Example: To calculate the fractional screen coordinates of the point [X,Y] GRAPH_X = (X - GPVAL_X_MIN) / (GPVAL_X_MAX - GPVAL_X_MIN) GRAPH_Y = (Y - GPVAL_Y_MIN) / (GPVAL_Y_MAX - GPVAL_Y_MIN) SCREEN_X = GPVAL_TERM_XMIN + GRAPH_X * (GPVAL_TERM_XMAX - GPVAL_TERM_XMIN) SCREEN_Y = GPVAL_TERM_YMIN + GRAPH_Y * (GPVAL_TERM_YMAX - GPVAL_TERM_YMIN) FRAC_X = SCREEN_X * GPVAL_TERM_SCALE / GPVAL_TERM_XSIZE FRAC_Y = SCREEN_Y * GPVAL_TERM_SCALE / GPVAL_TERM_YSIZE =errors =error state The read-only variable GPVAL_ERRNO is set to a non-zero value if any gnuplot command terminates early due to an error. The most recent error message is stored in the string variable GPVAL_ERRMSG. Both GPVAL_ERRNO and GPVAL_ERRMSG can be cleared using the command `reset errors`. Interactive terminals with `mouse` functionality maintain read-only variables with the prefix "MOUSE_". See `mouse variables` for details. The `fit` mechanism uses several variables with names that begin "FIT_". It is safest to avoid using such names. When using `set fit errorvariables`, the error for each fitted parameter will be stored in a variable named like the parameter, but with "_err" appended. See the documentation on `fit` and `set fit` for details. See `user-defined variables`, `reset errors`, `mouse variables`, and `fit`. 3 User-defined variables and functions ?expressions user-defined ?functions user-defined ?user-defined variables ?user-defined ?variables New user-defined variables and functions of one through twelve variables may be declared and used anywhere, including on the `plot` command itself. User-defined function syntax: ( {,} ... {,} ) = where is defined in terms of through . This form of function definition is limited to a single line. More complicated multi-line functions can be defined using the function block mechanism (new in this version). See `function blocks`. User-defined variable syntax: = Examples: w = 2 q = floor(tan(pi/2 - 0.1)) f(x) = sin(w*x) sinc(x) = sin(pi*x)/(pi*x) delta(t) = (t == 0) ramp(t) = (t > 0) ? t : 0 min(a,b) = (a < b) ? a : b comb(n,k) = n!/(k!*(n-k)!) len3d(x,y,z) = sqrt(x*x+y*y+z*z) plot f(x) = sin(x*a), a = 0.2, f(x), a = 0.4, f(x) file = "mydata.inp" file(n) = sprintf("run_%d.dat",n) The final two examples illustrate a user-defined string variable and a user-defined string function. =NaN =pi Note that the variables `pi` (3.14159...) and `NaN` (IEEE "Not a Number") are already defined. You can redefine these to something else if you really need to. The original values can be recovered by setting: NaN = GPVAL_NaN pi = GPVAL_pi Other variables may be defined under various gnuplot operations like mousing in interactive terminals or fitting; see `gnuplot-defined variables` for details. You can check for existence of a given variable V by the exists("V") expression. For example a = 10 if (exists("a")) print "a is defined" if (!exists("b")) print "b is not defined" Valid names are the same as in most programming languages: they must begin with a letter, but subsequent characters may be letters, digits, or "_". Each function definition is made available as a special string-valued variable with the prefix 'GPFUN_'. Example: set label GPFUN_sinc at graph .05,.95 See `show functions`, `functions`, `gnuplot-defined variables`, `macros`, `value`. 3 arrays ?arrays =cardinality Arrays are implemented as indexed lists of user variables. The elements in an array are not limited to a single type of variable. Arrays must be created explicitly before being referenced. The size of an array cannot be changed after creation. Array elements are initially undefined unless they are provided in the array declaragion. In most places an array element can be used instead of a named user variable. The cardinality (number of elements) of array A is given by the expression |A|. Examples: array A[6] A[1] = 1 A[2] = 2.0 A[3] = {3.0, 3.0} A[4] = "four" A[6] = A[2]**3 array B[6] = [ 1, 2.0, A[3], "four", , B[2]**3 ] array C = split("A B C D E F") do for [i=1:6] { print A[i], B[i] } 1 1 2.0 2.0 {3.0, 3.0} {3.0, 3.0} four four 8.0 8.0 Note: Arrays and variables share the same namespace. For example, assignment of a string to a variable named FOO will destroy any previously created array with name FOO. The name of an array can be used in a `plot`, `splot`, `fit`, or `stats` command. This is equivalent to providing a file in which column 1 holds the array index (from 1 to size), column 2 holds the value of real(A[i]) and column 3 holds the value of imag(A[i]). Example: array A[200] do for [i=1:200] { A[i] = sin(i * pi/100.) } plot A title "sin(x) in centiradians" When plotting the imaginary component of complex array values, it may be referenced either as imag(A[$1]) or as $3. These two commands are equivalent plot A using (real(A[$1])) : (imag(A[$1])) plot A using 2:3 4 Array functions ?arrays functions ?arrays slice ?slice =split Starting with gnuplot version 6, an array can be passed to a function or returned by a function. For example a simple dot-product function acting on two equal-sized numerical arrays could be defined: dot(A,B) = (|A| != |B|) ? NaN : sum [i=1:|A|] A[i] * B[i] Built-in functions that return an array include the slice operation array[min:max] and the index retrieval function index(Array,value). T = split("A B C D E F") U = T[3:4] print T [ "A", "B", "C", "D", "E", "F" ] print U [ "C", "D" ] print index( T, "D" ) 4 Note that T and U in this example are now arrays, whether or not they had been previously declared. 4 Array indexing ?arrays indexing =index Array indices run from 1 to N for an array with N elements. Element i of array A is accessed by A[i]. The built-in function `index(Array, )` returns an integer i such that A[i] is equal to , where may be any expression that evaluates to a number (integer, real, or complex) or a string. The array element must match in both type and value. A return of 0 indicates that no match was found. array A = [ 4.0, 4, "4" ] print index( A, 4 ) 2 print index( A, 2.+2. ) 1 print index( A, "D4"[2:2] ) 3 2 Fonts ?fonts Gnuplot does not provide any fonts of its own. It relies on external font handling, the details of which unfortunately vary from one terminal type to another. Brief documentation of font mechanisms that apply to more than one terminal type is given here. For information on font use by other individual terminals, see the documentation for that terminal. Although it is possible to include non-alphabetic symbols by temporarily switching to a special font, e.g. the Adobe Symbol font, the preferred method is now to choose UTF-8 encoding and treat the symbol like any other character. Alternatively you can specify the unicode entry point for the desired symbol as an escape sequence in enhanced text mode. See `encoding`, `unicode`, `locale`, and `escape sequences`. 3 cairo (pdfcairo, pngcairo, epscairo, wxt terminals) ?fonts cairo ?fontconfig ?fonts fontconfig =fonts =pdf =png =wxt Some terminals, including all the cairo-based terminals, access fonts via the fontconfig system library. Please see the ^ fontconfig user manual. ^ It is usually sufficient in gnuplot to request a font by a generic name and size, letting fontconfig substitute a similar font if necessary. The following will probably all work: set term pdfcairo font "sans,12" set term pdfcairo font "Times,12" set term pdfcairo font "Times-New-Roman,12" 3 gd (png, gif, jpeg, sixel terminals) ?gd ?fonts gd =fonts =png =jpeg =gif =sixel Font handling for the png, gif, jpeg, and sixelgd terminals is done by the libgd library. At a minimum it provides five basic fonts named `tiny`, `small`, `medium`, `large`, and `giant` that cannot be scaled or rotated. Use one of these keywords instead of the `font` keyword. E.g. set term png tiny On many systems libgd can also use generic font handling provided by the fontconfig tools (see `fontconfig`). On most systems without fontconfig, libgd provides access to Adobe fonts (*.pfa *.pfb) and to TrueType fonts (*.ttf). You must give the name of the font file, not the name of the font inside it, in the form " {,}". is either the full pathname to the font file, or the first part of a filename in one of the directories listed in the GDFONTPATH environmental variable. That is, 'set term png font "Face"' will look for a font file named either /Face.ttf or /Face.pfa. For example, if GDFONTPATH contains `/usr/local/fonts/ttf:/usr/local/fonts/pfa` then the following pairs of commands are equivalent set term png font "arial" set term png font "/usr/local/fonts/ttf/arial.ttf" set term png font "Helvetica" set term png font "/usr/local/fonts/pfa/Helvetica.pfa" To request a default font size at the same time: set term png font "arial,11" If no specific font is requested in the "set term" command, gnuplot checks the environmental variable GNUPLOT_DEFAULT_GDFONT. 3 postscript (also encapsulated postscript *.eps) ?fonts postscript =fonts =postscript =eps PostScript font handling is done by the printer or viewing program. Gnuplot can create valid PostScript or encapsulated PostScript (*.eps) even if no fonts at all are installed on your computer. Gnuplot simply refers to the font by name in the output file, and assumes that the printer or viewing program will know how to find or approximate a font by that name. All PostScript printers or viewers should know about the standard set of Adobe fonts `Times-Roman`, `Helvetica`, `Courier`, and `Symbol`. It is likely that many additional fonts are also available, but the specific set depends on your system or printer configuration. Gnuplot does not know or care about this; the output *.ps or *.eps files that it creates will simply refer to whatever font names you request. Thus set term postscript eps font "Times-Roman,12" will produce output that is suitable for all printers and viewers. On the other hand set term postscript eps font "Garamond-Premier-Pro-Italic" will produce a valid PostScript output file, but since it refers to a specialized font only some printers or viewers will be able to display the exact font that was requested. Most will substitute a different font. However, it is possible to embed a specific font in the output file so that all printers will be able to use it. This requires that the a suitable font description file is available on your system. Note that some font files require specific licensing if they are to be embedded in this way. See `postscript fontfile` for more detailed description and examples. 2 Glossary ?glossary =terminal =screen =record =block As `gnuplot` has evolved over more than 30 years, the meaning of certain words used in commands and in the documentation may have diverged from current common usage. This section explains how some of these terms are used in `gnuplot`. The term "terminal" refers to an output mode, not to the thing you are typing on. For example, the command `set terminal pdf` means that subsequent plotting commands will produce pdf ouput. Usually you would want to accompany this with a `set output "filename"` command to control where the pdf output is written. A "page" or "screen" or "canvas" is the entire area addressable by `gnuplot`. On a desktop it is a full window; on a plotter, it is a single sheet of paper. When discussing data files, the term "record" denotes a single line of text in the file, that is, the characters between newline or end-of-record characters. A "point" is the datum extracted from a single record. A "block" of data is a set of consecutive records delimited by blank lines. A line, when referred to in the context of a data file, is a subset of a block. Note that the term "data block" may also be used to refer to a named block of inline data (see `datablocks`). 2 inline data and datablocks ?inline data ?inline ?data inline ?datablocks ?data datablocks There are two mechanisms for embedding data into a stream of gnuplot commands. If the special filename '-' appears in a plot command, then the lines immediately following the plot command are interpreted as inline data. See `special-filenames`. Data provided in this way can only be used once, by the plot command it follows. The second mechanism defines a named data block as a here-document. The named data is persistent and may be referred to by more than one plot command. Example: $Mydata << EOD 11 22 33 first line of data 44 55 66 second line of data # comments work just as in a data file 77 88 99 EOD stats $Mydata using 1:3 plot $Mydata using 1:3 with points, $Mydata using 1:2 with impulses Data block names must begin with a $ character, which distinguishes them from other types of persistent variables. The end-of-data delimiter (EOD in the example) may be any sequence of alphanumeric characters. For a parallel mechanism that stores executable commands rather than data in a named block, see `function blocks`. The storage associated with named data blocks can be released using `undefine` command. `undefine $*` frees all named data and function blocks at once. 2 iteration ?iteration ?iterate Ffigure_newsyntax gnuplot supports command iteration and block-structured if/else/while/do constructs. See `if`, `while`, and `do`. Simple iteration is possible inside `plot` or `set` commands. See `plot for`. General iteration spanning multiple commands is possible using a block construct as shown below. For a related new feature, see the `summation` expression type. Here is an example using several of these new syntax features: set multiplot layout 2,2 fourier(k, x) = sin(3./2*k)/k * 2./3*cos(k*x) do for [power = 0:3] { TERMS = 10**power set title sprintf("%g term Fourier series",TERMS) plot 0.5 + sum [k=1:TERMS] fourier(k,x) notitle } unset multiplot =iteration-specifier Iteration is controlled by an iteration specifier with syntax for [ in "string of N elements"] or for [ = : { : }] In the first case is a string variable that successively evaluates to single-word substrings 1 to N of the string in the iteration specifier. In the second case , , and are integers or integer expressions. =scope The scope of the iteration variable is private to that iteration. See `scope`. You cannot permanently change the value of the iteration variable inside the iterated clause. If the iteration variable has a value prior to iteration, that value will be retained or restored at the end of the iteration. For example, the following commands will print 1 2 3 4 5 6 7 8 9 10 A. i = "A" do for [i=1:10] { print i; i=10; } print i 2 linetypes, colors, and styles ?linetypes ?colors In very old gnuplot versions, each terminal type provided a set of distinct "linetypes" that could differ in color, in thickness, in dot/dash pattern, or in some combination of color and dot/dash. These colors and patterns were not guaranteed to be consistent across different terminal types although most used the color sequence red/green/blue/magenta/cyan/yellow. You can select this old behaviour via the command `set colorsequence classic`, but by default gnuplot now uses a terminal-independent sequence of 8 colors. You can further customize the sequence of linetype properties interactively or in an initialization file. See `set linetype`. Several sample initialization files are provided in the distribution package. The current linetype properties for a particular terminal can be previewed by issuing the `test` command after setting the terminal type. Successive functions or datafiles plotted by a single command will be assigned successive linetypes in the current default sequence. You can override this for any individual function, datafile, or plot element by giving explicit line properties in the plot command. Examples: plot "foo", "bar" # plot two files using linetypes 1, 2 plot sin(x) linetype 4 # use linetype color 4 In general, colors can be specified using named colors, rgb (red, green, blue) components, hsv (hue, saturation, value) components, or a coordinate along the current pm3d palette. The keyword `linecolor` may be abbreviated to `lc`. Examples: plot sin(x) lc rgb "violet" # use one of gnuplot's named colors plot sin(x) lc rgb "#FF00FF" # explicit RGB triple in hexadecimal plot sin(x) lc palette cb -45 # whatever color corresponds to -45 # in the current cbrange of the palette plot sin(x) lc palette frac 0.3 # fractional value along the palette See `colorspec`, `show colornames`, `hsv`, `set palette`, `cbrange`. See also `set monochrome`. Linetypes also have an associated dot-dash pattern although not all terminal types are capable of using it. You can specify the dot-dash pattern independent of the line color. See `dashtype`. 3 colorspec ?colorspec =colors ?lc ?linecolor ?tc ?textcolor =fillcolor Many commands allow you to specify a linetype with an explicit color. Syntax: ... {linecolor | lc} {"colorname" | | } ... {textcolor | tc} { | {linetype | lt} } ... {fillcolor | fc} { | linetype | linestyle } where has one of the following forms: rgbcolor "colorname" # e.g. "blue" rgbcolor "0xRRGGBB" # string containing hexadecimal constant rgbcolor "0xAARRGGBB" # string containing hexadecimal constant rgbcolor "#RRGGBB" # string containing hexadecimal in x11 format rgbcolor "#AARRGGBB" # string containing hexadecimal in x11 format rgbcolor # integer value representing AARRGGBB rgbcolor variable # integer value is read from input file palette frac # runs from 0 to 1 palette cb # lies within cbrange palette z palette # use named colormap rather than current palette variable # color index is read from input file bgnd # background color black The "" is the linetype number the color of which is used, see `test`. "colorname" refers to one of the color names built in to gnuplot. For a list of the available names, see `show colornames`. Hexadecimal constants can be given in quotes as "#RRGGBB" or "0xRRGGBB", where RRGGBB represents the red, green, and blue components of the color and must be between 00 and FF. For example, magenta = full-scale red + full-scale blue could be represented by "0xFF00FF", which is the hexadecimal representation of (255 << 16) + (0 << 8) + (255). "#AARRGGBB" represents an RGB color with an alpha channel (transparency) value in the high bits. An alpha value of 0 represents a fully opaque color; i.e., "#00RRGGBB" is the same as "#RRGGBB". An alpha value of 255 (FF) represents full transparency. For a callable function that converts any of these forms to a 32bit integer representation of the color, see `expressions functions rgbcolor`. The color palette is a linear gradient of colors that smoothly maps a single numerical value onto a particular color. Two such mappings are always in effect. `palette frac` maps a fractional value between 0 and 1 onto the full range of the color palette. `palette cb` maps the range of the color axis onto the same palette. See `set cbrange`. See also `set colorbox`. You can use either of these to select a constant color from the current palette. "palette z" maps the z value of each plot segment or plot element into the cbrange mapping of the palette. This allows smoothly-varying color along a 3d line or surface. It also allows coloring 2D plots by palette values read from an extra column of data (not all 2D plot styles allow an extra column). =bgnd =black There are two special color specifiers: `bgnd` for background color and `black`. 4 background color ?background ?bgnd Most terminals allow you to set an explicit background color for the plot. The special linetype `bgnd` will draw in this color, and `bgnd` is also recognized as a color. Examples: # This will erase a section of the canvas by writing over it in the # background color set term wxt background rgb "gray75" set object 1 rectangle from x0,y0 to x1,y1 fillstyle solid fillcolor bgnd # Draw an "invisible" line at y=0, erasing whatever was underneath plot 0 lt bgnd 4 linecolor variable ?linecolor variable ?lc variable ?textcolor variable ?tc variable ?variable linecolor `lc variable` tells the program to use the value read from one column of the input data as a linetype index, and use the color belonging to that linetype. This requires a corresponding additional column in the `using` specifier. Text colors can be set similarly using `tc variable`. Examples: # Use the third column of data to assign colors to individual points plot 'data' using 1:2:3 with points lc variable # A single data file may contain multiple sets of data, separated by two # blank lines. Each data set is assigned as index value (see `index`) # that can be retrieved via the `using` specifier `column(-2)`. # See `pseudocolumns`. This example uses to value in column -2 to # draw each data set in a different line color. plot 'data' using 1:2:(column(-2)) with lines lc variable 4 palette ?colorspec palette Syntax ... {lc|fc|tc} palette {z} ... {lc|fc|tc} palette frac ... {lc|fc|tc} palette cb ... fc palette The palette defines a range of colors with gray values between 0 and 1. `palette frac ` selects the color with gray value . `palette cb ` selects the single color whose fractional gray value is (z - cbmin) / (cbmax - cbmin). `palette` and `palette z` both map the z coordinate of the plot element being colored onto the current palette. If z is outside cbrange it is by default mapped to palette fraction 0 or palette franction 1. If the option `set pm3d noclipcb` is set, then quadrangles in a pm3d plot whose z values are out of range will not be drawn at all. `fillcolor palette ` maps the z coordinate of a plot element onto a previously saved named colormap instead of using the current palette. See `set colormap`. If the colormap has a separate range associated with it, that range is used to map z values analogous to the use of cbrange to map the standard palette. If there is no separate range for this colormap then cbrange is used. 4 rgbcolor variable ?rgbcolor variable ?lc rgbcolor variable ?tc rgbcolor variable ?variable rgbcolor ?variable textcolor You can assign a separate color for each data point, line segment, or label in your plot. `lc rgbcolor variable` tells the program to read RGB color information for each line in the data file. This requires a corresponding additional column in the `using` specifier. The extra column is interpreted as a 24-bit packed RGB triple. If the value is provided directly in the data file it is easiest to give it as a hexadecimal value (see `rgbcolor`). Alternatively, the `using` specifier can contain an expression that evaluates to a 24-bit RGB color as in the example below. Text colors are similarly set using `tc rgbcolor variable`. Example: # Place colored points in 3D at the x,y,z coordinates corresponding to # their red, green, and blue components rgb(r,g,b) = 65536 * int(r) + 256 * int(g) + int(b) splot "data" using 1:2:3:(rgb($1,$2,$3)) with points lc rgb variable 3 dashtype ?dashtype =dashtype The dash pattern (`dashtype`) is a separate property associated with each line, analogous to `linecolor` or `linewidth`. It is not necessary to place the current terminal in a special mode just to draw dashed lines. I.e. the old command `set term {solid|dashed}` is now ignored. All lines have the property `dashtype solid` unless you specify otherwise. You can change the default for a particular linetype using the command `set linetype` so that it affects all subsequent commands, or you can include the desired dashtype as part of the `plot` or other command. Syntax: dashtype N # predefined dashtype invoked by number dashtype "pattern" # string containing a combination of the characters # dot (.) hyphen (-) underscore(_) and space. dashtype (s1,e1,s2,e2,s3,e3,s4,e4) # dash pattern specified by 1 to 4 # numerical pairs , Example: # Two functions using linetype 1 but distinguished by dashtype plot f1(x) with lines lt 1 dt solid, f2(x) with lines lt 1 dt 3 Some terminals support user-defined dash patterns in addition to whatever set of predefined dash patterns they offer. Examples: plot f(x) dt 3 # use terminal-specific dash pattern 3 plot f(x) dt ".. " # construct a dash pattern on the spot plot f(x) dt (2,5,2,15) # numerical representation of the same pattern set dashtype 11 (2,4,4,7) # define new dashtype to be called by index plot f(x) dt 11 # plot using our new dashtype If you specify a dash pattern using a string the program will convert this to a sequence of , pairs. Dot "." becomes (2,5), dash "-" becomes (10,10), underscore "_" becomes (20,10), and each space character " " adds 10 to the previous value. The command `show dashtype` will show both the original string and the converted numerical sequence. 3 linestyles vs linetypes ?linestyles vs linetypes A `linestyle` is a temporary association of properties linecolor, linewidth, dashtype, and pointtype. It is defined using the command `set style line`. Once you have defined a linestyle, you can use it in a plot command to control the appearance of one or more plot elements. In other words, it is just like a linetype except for its lifetime. Whereas `linetypes` are permanent (they last until you explicitly redefine them), `linestyles` last until the next reset of the graphics state. Examples: # define a new line style with terminal-independent color cyan, # linewidth 3, and associated point type 6 (a circle with a dot in it). set style line 5 lt rgb "cyan" lw 3 pt 6 plot sin(x) with linespoints ls 5 # user-defined line style 5 3 special linetypes ?linetypes special linetypes ?special_linetypes ?nodraw =bgnd =background =black A few special (non-numerical) linetypes are recognized. `lt black` specifies a solid black line. `lt bgnd` specifies a solid line with the background color of the current terminal. See `background`. `lt nodraw` skips drawing the line altogether. This is useful in conjunction with plot style `linespoints`. It allows you to suppress the line component of the plot while retaining point properties that are available only in this plot style. For example plot f(x) with linespoints lt nodraw pointinterval -3 will draw only every third point and will isolate it by placing a small circle of background color underneath it. See `linespoints`. `lt nodraw` may also be used to suppress a particular set of lines that would otherwise be drawn automatically. For example you could suppress certain contour levels in a contour plot by setting their linetype to `nodraw`. 2 layers ?layers ?behind ?front ?back A gnuplot plot is built up by drawing its various components in a fixed order. This order can be modified by assigning some components to a specific layer using the keywords `behind`, `back`, or `front`. For example, to replace the background color of the plot area you could define a colored rectangle with the attribute `behind`. set object 1 rectangle from graph 0,0 to graph 1,1 fc rgb "gray" behind The order of drawing is behind back the plot itself the plot legend (`key`) front Within each layer elements are drawn in the order grid, axis, and border elements pixmaps in numerical order objects (rectangles, circles, ellipses, polygons) in numerical order labels in numerical order arrows in numerical order In the case of multiple plots on a single page (multiplot mode) this order applies separately to each component plot, not to the multiplot as a whole. An exception to this is that several TeX-based terminals (e.g. pslatex, cairolatex) accumulate all text elements in one output stream and graphics in a separate output stream; the text and graphics are then combined to yield the final figure. In general this leaves each text element either completely behind or completely in front of the graphics. 2 mouse input ?mouse input Many terminals allow interaction with the current plot using the mouse. Some also support the definition of hotkeys to activate pre-defined functions by hitting a single key while the mouse focus is in the active plot window. It is even possible to combine mouse input with `batch` command scripts, by invoking the command `pause mouse` and then using the mouse variables returned by mouse clicking as parameters for subsequent scripted actions. See `bind` and `mouse variables`. See also the command `set mouse`. 3 bind ?commands bind ?hotkey ?hotkeys ?bind Syntax: bind {allwindows} [] [""] bind "" reset bind The `bind` allows defining or redefining a hotkey, i.e. a sequence of gnuplot commands which will be executed when a certain key or key sequence is pressed while the driver's window has the input focus. Note that `bind` is only available if gnuplot was compiled with `mouse` support and it is used by all mouse-capable terminals. A user-specified binding supersedes any builtin bindings, except that and 'q' cannot normally be rebound. For an exception, see `bind space`. Mouse button bindings are only active in 2D plots. You get the list of all hotkeys by typing `show bind` or `bind` or by typing the hotkey 'h' in the graph window. Key bindings are restored to their default state by `reset bind`. Note that multikey-bindings with modifiers must be given in quotes. Normally hotkeys are only recognized when the currently active plot window has focus. `bind allwindows ...` (short form: `bind all ...`) causes the binding for to apply to all gnuplot plot windows, active or not. In this case gnuplot variable MOUSE_KEY_WINDOW is set to the ID of the originating window, and may be used by the bound command. Examples: - set bindings: bind a "replot" bind "ctrl-a" "plot x*x" bind "ctrl-alt-a" 'print "great"' bind Home "set view 60,30; replot" bind all Home 'print "This is window ",MOUSE_KEY_WINDOW' - show bindings: bind "ctrl-a" # shows the binding for ctrl-a bind # shows all bindings show bind # show all bindings - remove bindings: bind "ctrl-alt-a" "" # removes binding for ctrl-alt-a (note that builtins cannot be removed) reset bind # installs default (builtin) bindings - bind a key to toggle something: v=0 bind "ctrl-r" "v=v+1;if(v%2)set term x11 noraise; else set term x11 raise" Modifiers (ctrl / alt) are case insensitive, keys not: ctrl-alt-a == CtRl-alT-a ctrl-alt-a != ctrl-alt-A List of modifiers (alt == meta): ctrl, alt, shift (only valid for Button1 Button2 Button3) List of supported special keys: "BackSpace", "Tab", "Linefeed", "Clear", "Return", "Pause", "Scroll_Lock", "Sys_Req", "Escape", "Delete", "Home", "Left", "Up", "Right", "Down", "PageUp", "PageDown", "End", "Begin", "KP_Space", "KP_Tab", "KP_Enter", "KP_F1", "KP_F2", "KP_F3", "KP_F4", "KP_Home", "KP_Left", "KP_Up", "KP_Right", "KP_Down", "KP_PageUp", "KP_PageDown", "KP_End", "KP_Begin", "KP_Insert", "KP_Delete", "KP_Equal", "KP_Multiply", "KP_Add", "KP_Separator", "KP_Subtract", "KP_Decimal", "KP_Divide", "KP_1" - "KP_9", "F1" - "F12" The following are window events rather than actual keys "Button1" "Button2" "Button3" "Close" See also help for `mouse`. 4 bind space ?commands bind space ?bind space If gnuplot was built with configuration option --enable-raise-console, then typing in the plot window raises gnuplot's command window. Maybe. In practice this is highly system-dependent. This hotkey can be changed to ctrl-space by starting gnuplot as 'gnuplot -ctrlq', or by setting the XResource 'gnuplot*ctrlq'. 3 Mouse variables ?mouse variables When `mousing` is active, clicking in the active window will set several user variables that can be accessed from the gnuplot command line. The coordinates of the mouse at the time of the click are stored in MOUSE_X MOUSE_Y MOUSE_X2 and MOUSE_Y2. The mouse button clicked, and any meta-keys active at that time, are stored in MOUSE_BUTTON MOUSE_SHIFT MOUSE_ALT and MOUSE_CTRL. These variables are set to undefined at the start of every plot, and only become defined in the event of a mouse click in the active plot window. To determine from a script if the mouse has been clicked in the active plot window, it is sufficient to test for any one of these variables being defined. plot 'something' pause mouse if (exists("MOUSE_BUTTON")) call 'something_else'; \ else print "No mouse click." It is also possible to track keystrokes in the plot window using the mousing code. plot 'something' pause mouse keypress print "Keystroke ", MOUSE_KEY, " at ", MOUSE_X, " ", MOUSE_Y When `pause mouse keypress` is terminated by a keypress, then MOUSE_KEY will contain the ascii character value of the key that was pressed. MOUSE_CHAR will contain the character itself as a string variable. If the pause command is terminated abnormally (e.g. by ctrl-C or by externally closing the plot window) then MOUSE_KEY will equal -1. Note that after a zoom by mouse, you can read the new ranges as GPVAL_X_MIN, GPVAL_X_MAX, GPVAL_Y_MIN, and GPVAL_Y_MAX, see `gnuplot-defined variables`. 2 Persist ?persist Many gnuplot terminals (aqua, pm, qt, x11, windows, wxt, ...) open separate display windows on the screen into which plots are drawn. The `persist` option tells gnuplot to leave these windows open when the main program exits. It has no effect on non-interactive terminal output. For example if you issue the command gnuplot -persist -e 'plot sinh(x)' gnuplot will open a display window, draw the plot into it, and then exit, leaving the display window containing the plot on the screen. You can also specify `persist` or `nopersist` when you set a new terminal. set term qt persist size 700,500 Depending on the terminal type, some mousing operations may still be possible in the persistent window. However operations like zoom/unzoom that require redrawing the plot are not possible because the main program has exited. If you want to leave a plot window open and fully mouseable after creating the plot, for example when running gnuplot from a script file rather than interactively, see `pause mouse close`. 2 Plotting ?plotting There are four `gnuplot` commands which actually create a plot: `plot`, `splot`, `replot`, and `refresh`. Other commands control the layout, style, and content of the plot that will eventually be created. `plot` generates 2D plots. `splot` generates 3D plots (actually 2D projections, of course). `replot` reexecutes the previous `plot` or `splot` command. `refresh` is similar to `replot` but it reuses any previously stored data rather than rereading data from a file or input stream. =multiplot =inset =subfigures Each time you issue one of these four commands it will redraw the screen or generate a new page of output containing all of the currently defined axes, labels, titles, and all of the various functions or data sources listed in the original plot command. If instead you need to place several complete plots next to each other on the same page, e.g. to make a panel of sub-figures or to inset a small plot inside a larger plot, use the command `set multiplot` to suppress generation of a new page for each plot command. Much of the general information about plotting can be found in the discussion of `plot`; information specific to 3D can be found in the `splot` section. `plot` operates in either rectangular or polar coordinates -- see `set polar`. `splot` operates in Cartesian coordinates, but will accept azimuthal or cylindrical coordinates on input. See `set mapping`. =axes `plot` also lets you use each of the four borders -- x (bottom), x2 (top), y (left) and y2 (right) -- as an independent axis. The `axes` option lets you choose which pair of axes a given function or data set is plotted against. A full complement of `set` commands exists to give you complete control over the scales and labeling of each axis. Some commands have the name of an axis built into their names, such as `set xlabel`. Other commands have one or more axis names as options, such as `set logscale xy`. Commands and options controlling the z axis have no effect on 2D graphs. `splot` can plot surfaces and contours in addition to points and/or lines. See `set isosamples` for information about defining the grid for a 3D function. See `splot datafile` for information about the requisite file structure for 3D data. For contours see `set contour`, `set cntrlabel`, and `set cntrparam`. In `splot`, control over the scales and labels of the axes are the same as with `plot` except that there is also a z axis and labeling the x2 and y2 axes is possible only for pseudo-2D plots created using `set view map`. 2 Plugins ?plugins The set of functions available for plotting or for evaluating expressions can be extended through a plugin mechanism that imports executable functions from a shared library. For example, gnuplot versions through 5.4 did not provide a built-in implementation of the upper incomplete gamma function Q(a,x). #TeX \\ $Q(a,x)=\frac{1}{\Gamma(x)}\intop_{x}^{\infty}t^{a-1}e^{-t}dt$ .\quad\quad You could define an approximation directly in gnuplot like this: Q(a,x) = 1. - igamma(a,x) However this has inherently limited precision as igamma(a,x) approaches 1. If you need a more accurate implementation, it would be better to provide one via a plugin (see below). Once imported, the function can be used just as any other built-in or user-defined function in gnuplot. See `import`. The gnuplot distribution includes source code and instructions for creating a plugin library in the directory demo/plugin. You can modify the simple example file `demo_plugin.c` by replacing one or more of the toy example functions with an implementation of the function you are interested in. This could include invocation of functions from an external mathematical library. The demo/plugin directory also contains source for a plugin that implements Q(a,x). As noted above, this plugin allows earlier versions of gnuplot to provide the same function `uigamma` as version 6. import Q(a,x) from "uigamma_plugin" uigamma(a,x) = ((x<1 || x plot FOO watch mouse set style watchpoints nolabels set style watchpoints label unset style watchpoints # return to default style show watchpoints # summarizes all watches from previous plot command A watchpoint is a target value for the x, y, or z coordinate or for a function f(x,y). Each watchpoint is attached to a single plot within a `plot` command. Watchpoints are tracked only for styles `with lines` and `with linespoints`. Every component line segment of that plot is checked against all watchpoints attached the plot to see whether one or more of the watchpoint targets is satisfied at a point along that line segment. A list of points that satisfy the the target condition ("hits") is accumulated as the plot is drawn. For example, if there is a watchpoint with a target y=100, each line segment is checked to see if the y coordinates of the two endpoints bracket the target y value. If so then some point [x,y] on the line segment satisfies the target condition y = 100 exactly. This target point is then found by linear interpolation or by iterative bisection. Watchpoints within a single plot command are numbered successively. More than one watchpoint per plot component may be specified. Example: plot DATA using 1:2 smooth cnormal watch y=0.25 watch y=0.5 watch y=0.75 Ffigure_watchpoints Watchpoint hits for each target in the previous plot command are stored in named arrays WATCH_n. You can also display a summary of all watchpoint hits from the previous plot command; see `show watchpoints`. gnuplot> show watchpoints Plot title: "DATA using 1:2 smooth cnormal" Watch 1 target y = 0.25 (1 hits) hit 1 x 49.7 y 0.25 Watch 2 target y = 0.5 (1 hits) hit 1 x 63.1 y 0.5 Watch 3 target y = 0.75 (1 hits) hit 1 x 67.8 y 0.75 Smoothing: Line segments are checked as they are drawn. For unsmoothed data plots this means a hit found by interpolation will lie exactly on a line segment connecting two data points. If a data plot is smoothed, hits will lie on a line segment from the smoothed curve. Depending on the quality of the smoothed fit, this may or may not be more accurate than the hit from the unsmoothed data. Accuracy: If the line segment was generated from a function plot, the exact value of x such that f(x) = y is found by iterative bisection. Otherwise the coordinates [x,y] are approximated by linear interpolation along the line segment. 3 watch mouse ?watchpoints mouse ?watch mouse Using the current mouse x coordinate as a watch target generates a label that moves along the line of the plot tracking the horizontal position of the mouse. This allows simultaneous readout of the y values of multiple plot lines in the same graph. The appearance of the point indicating the current position and of the label can be modified by `set style watchpoint` and `set style textbox` Example: set style watchpoint labels point pt 6 ps 2 boxstyle 1 set style textbox 1 lw 0.5 opaque plot for [i=1:N] "file.dat" using 1:(column(i)) watch mouse 3 watch labels ?watchpoint labels ?watch labels By default, labels are always generated for the target "watch mouse". You can turn labels on for other watch targets using the command `set style watchpoint labels`. The label text is "x : y", where x and y are the coordinates of the point, formatted using the current settings for the corresponding axes. Example: set y2tics format "%.2fÂ°" set style watchpoint labels point pt 6 plot FOO axes x1y2 watch mouse 1 Plotting styles ?plotting styles =plot styles Many plotting styles are available in gnuplot. They are listed alphabetically below. The commands `set style data` and `set style function` change the default plotting style for subsequent `plot` and `splot` commands. You can also specify the plot style explicitly as part of the `plot` or `splot` command. If you want to mix plot styles within a single plot, you must specify the plot style for each component. Example: plot 'data' with boxes, sin(x) with lines Each plot style has its own expected set of data entries in a data file. For example, by default the `lines` style expects either a single column of y values (with implicit x ordering) or a pair of columns with x in the first and y in the second. For more information on how to fine-tune how columns in a file are interpreted as plot data, see `using`. 2 arrows ?plotting styles arrows ?style arrows ?with arrows ?arrows ^figure_vectors The 2D `arrows` style draws an arrow with specified length and orientation angle at each point (x,y). Additional input columns may be used to provide variable (per-datapoint) color information or arrow style. It is identical to the 2D style `with vectors` except that each arrow head is positioned using length + angle rather than delta_x + delta_y. See `with vectors`. 4 columns: x y length angle The keywords `with arrows` may be followed by inline arrow style properties, a reference to a predefined arrow style, or `arrowstyle variable` to load the index of the desired arrow style for each arrow from a separate column. `length` > 0 is interpreted in x-axis coordinates. -1 < `length` < 0 is interpreted in horizontal graph coordinates; i.e. |length| is a fraction of the total graph width. The program will adjust for differences in x and y scaling or plot aspect ratio so that the visual length is independent of the orientation angle. `angle` is always specified in degrees. 3 arrowstyle variable ?arrowstyle variable ?variable arrowstyle For plot styles `with arrows` and `with vectors`, you can provide an extra column of input data that provides an integer arrow style corresponding to style previously defined using `set style arrow`. Example: set style arrow 1 head nofilled linecolor "blue" linewidth 0.5 set style arrow 2 head filled linecolor "red" linewidth 1.0 # column 5 is expected to contain either 1 or 2, # determining which of the two previous defined styles to use plot DATA using 1:2:3:4:5 with arrows arrowstyle variable #TeX \newpage 2 Bee swarm plots ?beeswarm ?bee swarm =jitter #TeX ~ Ffigure_jitter "Bee swarm" plots result from applying jitter to separate overlapping points. A typical use is to compare the distribution of y values exhibited by two or more categories of points, where the category determines the x coordinate. See the `set jitter` command for how to control the overlap criteria and the displacement pattern used for jittering. The plots in the figure were created by the same plot command but different jitter settings. set jitter plot $data using 1:2:1 with points lc variable 2 boxerrorbars ?plotting styles boxerrorbars ?style boxerrorbars ?with boxerrorbars ?boxerrorbars The `boxerrorbars` style is only relevant to 2D data plotting. It is a combination of the `boxes` and `yerrorbars` styles. It requires 3, 4, or 5 columns of data. An additional (4th, 5th or 6th) input column may be used to provide variable (per-datapoint) color information (see `linecolor` and `rgbcolor variable`). 3 columns: x y ydelta 4 columns: x y ydelta xdelta (xdelta <= 0 means use boxwidth) 5 columns: x y ylow yhigh xdelta (xdelta <= 0 means use boxwidth) Ffigure_boxerrorbars The boxwidth will come from the fourth column if the y errors are given as "ydelta" or from the fifth column if they are in the form of "ylow yhigh". If xdelta is zero or negative, the width of the box is controlled by the value previously given for boxwidth. See `set boxwidth`. A vertical error bar is drawn to represent the y error in the same way as for the `yerrorbars` style, either from y-ydelta to y+ydelta or from ylow to yhigh, depending on how many data columns are provided. The line style used for the error bar may be controlled using `set bars`. Otherwise the error bar will match the border of the box. DEPRECATED: Old versions of gnuplot treated `boxwidth = -2.0` as a special case for four-column data with y errors in the form "ylow yhigh". In this case boxwidth was adjusted to leave no gap between adjacent boxes. This treatment is retained for backward-compatibility but may be removed in a future version. 2 boxes ?plotting styles boxes ?style boxes ?with boxes ?boxes In 2D plots the `boxes` style draws a rectangle centered about the given x coordinate that extends from the x axis, i.e. from y=0 not from the graph border, to the given y coordinate. The width of the box can be provided in an additional input column or controlled by `set boxwidth`. Otherwise each box extends to touch the adjacent boxes. In 3D plots the `boxes` style draws a box centered at the given [x,y] coordinate that extends from the plane at z=0 to the given z coordinate. The width of the box on x can be provided in a separate input column or via `set boxwidth`. The depth of the box on y is controlled by `set boxdepth`. Boxes do not automatically expand to touch each other as in 2D plots. 3 2D boxes ?style boxes 2D ?boxes 2D `plot with boxes` uses 2 or 3 columns of basic data. Additional input columns may be used to provide information such as variable line or fill color. See `rgbcolor variable`. 2 columns: x y 3 columns: x y x_width Ffigure_boxes The width of the box is obtained in one of three ways. If the input data has a third column, this will be used to set the box width. Otherwise if a width has been set using the `set boxwidth` command, this will be used. If neither of these is available, the width of each box will be calculated so that it touches the adjacent boxes. The box interiors are drawn using the current fillstyle. Alternatively a fillstyle may be specified in the plot command. See `set style fill`. If no fillcolor is given in the plot command, the current line color is used. Examples: To plot a data file with solid filled boxes with a small vertical space separating them (bargraph): set boxwidth 0.9 relative set style fill solid 1.0 plot 'file.dat' with boxes To plot a sine and a cosine curve in pattern-filled boxes style with explicit fill color: set style fill pattern plot sin(x) with boxes fc 'blue', cos(x) with boxes fc 'gold' The sin plot will use pattern 0; the cos plot will use pattern 1. Any additional plots would cycle through the patterns supported by the terminal driver. 3 3D boxes ?style boxes 3D ?boxes 3D `splot with boxes` requires at least 3 columns of input data. Additional input columns may be used to provide information such as box width or fill color. 3 columns: x y z 4 columns: x y z [x_width or color] 5 columns: x y z x_width color The last column is used as a color only if the splot command specifies a variable color mode. Examples splot 'blue_boxes.dat' using 1:2:3 fc "blue" splot 'rgb_boxes.dat' using 1:2:3:4 fc rgb variable splot 'category_boxes.dat' using 1:2:3:4:5 lc variable In the first example all boxes are blue and have the width previously set by `set boxwidth`. In the second example the box width is still taken from `set boxwidth` because the 4th column is interpreted as a 24-bit RGB color. The third example command reads box width from column 4 and interprets the value in column 5 as an integer linetype from which the color is derived. Ffigure_3Dboxes By default boxes have no thickness; they consist of a single rectangle parallel to the xz plane at the specified y coordinate. You can change this to a true box with four sides and a top by setting a non-zero extent on y. See `set boxdepth`. 3D boxes are processed as pm3d quadrangles rather than as surfaces. Because of this the front/back order of drawing is not affected by `set hidden3d`. See `set pm3d`. In gnuplot version 6 the edges of the box are colored by the border color of the plot's fill style; this is a change from version 5. For best results use a combination of `set pm3d depthorder base` and `set pm3d lighting`. 2 boxplot ?plotting styles boxplot ?style boxplot ?with boxplot ?boxplot Ffigure_boxplot Boxplots are a common way to represent a statistical distribution of values. Quartile boundaries are determined such that 1/4 of the points have a value equal or less than the first quartile boundary, 1/2 of the points have a value equal or less than the second quartile (median) value, etc. A box is drawn around the region between the first and third quartiles, with a horizontal line at the median value. Whiskers extend from the box to user-specified limits. Points that lie outside these limits are drawn individually. Examples # Place a boxplot at x coordinate 1.0 representing the y values in column 5 plot 'data' using (1.0):5 # Same plot but suppress outliers and force the width of the boxplot to 0.3 set style boxplot nooutliers plot 'data' using (1.0):5:(0.3) By default only one boxplot is produced that represents all y values from the second column of the using specification. However, an additional (fourth) column can be added to the specification. If present, the values of that column will be interpreted as the discrete levels of a factor variable. As many boxplots will be drawn as there are levels in the factor variable. The separation between these boxplots is 1.0 by default, but it can be changed by `set style boxplot separation`. By default, the value of the factor variable is shown as a tic label below (or above) each boxplot. Example # Suppose that column 2 of 'data' contains either "control" or "treatment" # The following example produces two boxplots, one for each level of the # factor plot 'data' using (1.0):5:(0):2 The default width of the box can be set via `set boxwidth ` or may be specified as an optional 3rd column in the `using` clause of the plot command. The first and third columns (x coordinate and width) are normally provided as constants rather than as data columns. By default the whiskers extend from the ends of the box to the most distant point whose y value lies within 1.5 times the interquartile range. By default outliers are drawn as circles (point type 7). The width of the bars at the end of the whiskers may be controlled using `set bars` or `set errorbars`. These default properties may be changed using the `set style boxplot` command. See `set style boxplot`, `bars`, `boxwidth`, `fillstyle`, `candlesticks`. 2 boxxyerror ?plotting styles boxxyerror ?style boxxyerror ?with boxxyerror ?boxxyerror Ffigure_boxxyerror The `boxxyerror` plot style is only relevant to 2D data plotting. It is similar to the `xyerrorbars` style except that it draws rectangular areas rather than crosses. It uses either 4 or 6 basic columns of input data. An additional (5th or 7th) input column may be used to provide variable (per-datapoint) color information (see `linecolor` and `rgbcolor variable`). 4 columns: x y xdelta ydelta 6 columns: x y xlow xhigh ylow yhigh The box width and height are determined from the x and y errors in the same way as they are for the `xyerrorbars` style---either from xlow to xhigh and from ylow to yhigh, or from x-xdelta to x+xdelta and from y-ydelta to y+ydelta, depending on how many data columns are provided. The 6 column form of the command provides a convenient way to plot rectangles with arbitrary x and y bounds. The interior of the boxes is drawn according to the current fillstyle. See `set style fill` and `boxes` for details. Alternatively a new fillstyle may be specified in the plot command. 2 candlesticks ?plotting styles candlesticks ?style candlesticks ?with candlesticks ?candlesticks Ffigure_candlesticks The `candlesticks` style can be used for 2D data plotting of financial data or for generating box-and-whisker plots of statistical data. The symbol is a rectangular box, centered horizontally at the x coordinate and limited vertically by the opening and closing prices. A vertical line segment at the x coordinate extends up from the top of the rectangle to the high price and another down to the low. The vertical line will be unchanged if the low and high prices are interchanged. Five columns of basic data are required: financial data: date open low high close whisker plot: x box_min whisker_min whisker_high box_high The width of the rectangle can be controlled by the `set boxwidth` command. For backwards compatibility with earlier gnuplot versions, when the boxwidth parameter has not been set then the width of the candlestick rectangle is taken from `set errorbars `. Alternatively, an explicit width for each box-and-whiskers grouping may be specified in an optional 6th column of data. The width must be given in the same units as the x coordinate. An additional (6th, or 7th if the 6th column is used for width data) input column may be used to provide variable (per-datapoint) color information (see `linecolor` and `rgbcolor variable`). By default the vertical line segments have no crossbars at the top and bottom. If you want crossbars, which are typically used for box-and-whisker plots, then add the keyword `whiskerbars` to the plot command. By default these whiskerbars extend the full horizontal width of the candlestick, but you can modify this by specifying a fraction of the full width. The usual convention for financial data is that the rectangle is empty if (open < close) and solid fill if (close < open). This is the behavior you will get if the current fillstyle is set to "empty". See `fillstyle`. If you set the fillstyle to solid or pattern, then this will be used for all boxes independent of open and close values. See also `set errorbars` and `financebars`. See also the ^ candlestick ^ and ^ finance ^ demos. Note: To place additional symbols or lines on a box-and-whisker plot requires additional plot components. The first example below uses a second component that squashes the candlestick onto a single line placed at the median value. # Data columns:X Min 1stQuartile Median 3rdQuartile Max set errorbars 4.0 set style fill empty plot 'stat.dat' using 1:3:2:6:5 with candlesticks title 'Quartiles', \ '' using 1:4:4:4:4 with candlesticks lt -1 notitle # Plot with crossbars on the whiskers, crossbars are 50% of full width plot 'stat.dat' using 1:3:2:6:5 with candlesticks whiskerbars 0.5 See `set boxwidth`, `set errorbars`, `set style fill`, and `boxplot`. 2 circles ?plotting styles circles ?style circles ?with circles ?circles Ffigure_circles The `circles` style plots a circle with an explicit radius at each data point. The radius is always interpreted in the units of the plot's horizontal axis (x or x2). The scale on y and the aspect ratio of the plot are both ignored. If the radius is not given in a separate column for each point it is taken from `set style circle`. In this case the radius may use graph or screen coordinates. Many combinations of per-point and previously set properties are possible. For 2D plots these include using x:y using x:y:radius using x:y:color using x:y:radius:color using x:y:radius:arc_begin:arc_end using x:y:radius:arc_begin:arc_end:color By default a full circle will be drawn. The result is similar to using a `points` plot with variable size points and pointtype 7, except that the circles scale with the x axis range. It is possible to instead plot arc segments by specifying a start and end angle (in degrees) in columns 4 and 5. A per-circle color may be provided in the last column of the using specifier. In this case the plot command must include a corresponding variable color term such as `lc variable` or `fillcolor rgb variable`. See `set style circle`, `set object circle`, and `set style fill`. For 3D plots the using specifier must contain splot DATA using x:y:z:radius:color where the variable color column is optional. Examples: # draws circles whose area is proportional to the value in column 3 set style fill transparent solid 0.2 noborder plot 'data' using 1:2:(sqrt($3)) with circles, \ 'data' using 1:2 with linespoints # draws Pac-men instead of circles plot 'data' using 1:2:(10):(40):(320) with circles Ffigure_piechart =piechart # draw a pie chart with inline data set xrange [-15:15] set style fill transparent solid 0.9 noborder plot '-' using 1:2:3:4:5:6 with circles lc var 0 0 5 0 30 1 0 0 5 30 70 2 0 0 5 70 120 3 0 0 5 120 230 4 0 0 5 230 360 5 e 2 contourfill ?plotting styles contourfill ?style contourfill ?with contourfill ?contourfill Ffigure_contourfill Contourfill is a 3D plotting style used to color a pm3d surface in slices along the z axis. It can be used in 2D projection (`set view map`) to create 2D contour plots with solid color between contour lines. The slice boundaries and the assigned colors are both controlled using `set contourfill`. See also `pm3d`, `zclip`. This style can be combined with `set contours` to superimpose contour lines that bound the slices. Care must be taken that the slice boundaries from `set contourfill` match the contour bounaries from `set cntrparam`. # slice boundaries determined by ztics # coloring set by palette mapping the slice midpoint z value set pm3d border retrace set contourfill ztics set ztics -20, 5, 20 set contour set cntrparam cubic levels increment -20, 5, 20 set cntrlabel onecolor set view map splot g(x,y) with contourfill, g(x,y) with lines nosurface 2 ellipses ?plotting styles ellipses ?style ellipses ?with ellipses ?ellipses Ffigure_ellipses The `ellipses` style plots an ellipse at each data point. This style is only relevant for 2D plotting. Each ellipse is described in terms of its center, major and minor diameters, and the angle between its major diameter and the x axis. 2 columns: x y 3 columns: x y diam (used for both major and minor axes) 4 columns: x y major_diam minor_diam 5 columns: x y major_diam minor_diam angle If only two input columns are present, they are taken as the coordinates of the centers, and the ellipses will be drawn with the default extent (see `set style ellipse`). The orientation of the ellipse, which is defined as the angle between the major diameter and the plot's x axis, is taken from the default ellipse style (see `set style ellipse`). If three input columns are provided, the third column is used for both diameters. The orientation angle defaults to zero. If four columns are present, they are interpreted as x, y, major diameter, minor diameter. Note that these are diameters, not radii. If either diameter is negative, both diameters will be taken from the default set by `set style ellipse`. An optional 5th column may specify the orientation angle in degrees. The ellipses will also be drawn with their default extent if either of the supplied diameters in the 3-4-5 column form is negative. In all of the above cases, optional variable color data may be given in an additional last (3th, 4th, 5th or 6th) column. See `colorspec`. `units keyword:` If `units xy` is included in the plot specification, the major diameter is interpreted in the units of the plot's horizontal axis (x or x2) while the minor diameter in that of the vertical axis (y or y2). If the x and y axis scales are not equal, the major/minor diameter ratio will no longer be correct after rotation. `units xx` interprets both diameters in units of the x axis. `units yy` interprets both diameters in units of the y axis. In the latter two cases the ellipses will have the correct aspect ratio even if the plot is resized. If `units` is omitted from the plot command, the setting from `set style ellipse` will be used. Example (draws ellipses, cycling through the available line types): plot 'data' using 1:2:3:4:(0):0 with ellipses See also `set object ellipse`, `set style ellipse` and `fillstyle`. 2 dots ?plotting styles dots ?style dots ?with dots ?dots Ffigure_dots The `dots` style plots a tiny dot at each point; this is useful for scatter plots with many points. Either 1 or 2 columns of input data are required in 2D. Three columns are required in 3D. For some terminals (post, pdf) the size of the dot can be controlled by changing the linewidth. 1 column y # x is row number 2 columns: x y 3 columns: x y z # 3D only (splot) 2 filledcurves ?plotting styles filledcurves ?style filledcurves ?with filledcurves ?filledcurves Ffigure_filledcurves The `filledcurves` style is only used for 2D plotting. It has three variants. The first two variants require either a single function or two columns (x,y) of input data, and may be further modified by the options listed below. Syntax: plot ... with filledcurves [option] where the option can be one of the following closed {above|below} x1 x2 y r= xy=, between The first variant, `closed`, treats the curve itself as a closed polygon. This is the default if there are two columns of input data. filledcurves closed ... just filled closed curve, The second variant is to fill the area between the curve and a given axis, a horizontal or vertical line, or a point. This can be further restricted to filling the area above or below the specified line. filledcurves x1 ... x1 axis, filledcurves x2 ... x2 axis, etc for y1 and y2 axes, filledcurves y=42 ... line at y=42, i.e. parallel to x axis, filledcurves xy=10,20 ... point 10,20 of x1,y1 axes (arc-like shape). filledcurves above r=1.5 the area of a polar plot outside radius 1.5 Ffigure_yerrorfill The third variant fills the area between two curves sampled at the same set of x coordinates. It requires three columns of input data (x, y1, y2). This is the default if there are three or more columns of input data. If you have a y value in column 2 and an associated error value in column 3 the area of uncertainty can be represented by shading. See also the similar 3D plot style `zerrorfill`. 3 columns: x y yerror plot $DAT using 1:($2-$3):($2+$3) with filledcurves, \ $DAT using 1:2 smooth mcs with lines The `above` and `below` options apply both to commands of the form ... filledcurves above {x1|x2|y|r}= and to commands of the form ... using 1:2:3 with filledcurves below In either case the option limits the filled area to one side of the bounding line or curve. Zooming a filled curve drawn from a datafile may produce empty or incorrect areas because gnuplot is clipping points and lines, and not areas. If the values , , or are outside the drawing boundary they are moved to the graph boundary. Then the actual fill area in the case of option xy=, will depend on xrange and yrange. 3 fill properties ?filledcurves border =border Plotting `with filledcurves` can be further customized by giving a fillstyle (solid/transparent/pattern) or a fillcolor. If no fillstyle (`fs`) is given in the plot command then the current default fill style is used. See `set style fill`. If no fillcolor (`fc`) is given in the plot command, the current line color is used. The {{no}border} property of the fillstyle is honored by filledcurves mode `closed`, the default. It is ignored by all other filledcurves modes. Example: plot 'data' with filledcurves fc "cyan" fs solid 0.5 border lc "blue" 2 financebars ?plotting styles financebars ?style financebars ?with financebars ?financebars The `financebars` style is only relevant for 2D data plotting of financial data. It requires 1 x coordinate (usually a date) and 4 y values (prices). 5 columns: date open low high close An additional (6th) input column may be used to provide variable (per-record) color information (see `linecolor` and `rgbcolor variable`). Ffigure_financebars The symbol is a vertical line segment, located horizontally at the x coordinate and limited vertically by the high and low prices. A horizontal tic on the left marks the opening price and one on the right marks the closing price. The length of these tics may be changed by `set errorbars`. The symbol will be unchanged if the high and low prices are interchanged. See `set errorbars` and `candlesticks`, and also the ^ finance demo. ^ 2 fillsteps ?style fillsteps ?with fillsteps ?fillsteps plot with fillsteps {above|below} {y=} Ffigure_steps The `fillsteps` style is only relevant to 2D plotting. It is exactly like the style `steps` except that the area between the curve and the baseline (default y=0) is filled in the current fill style. The options `above` and `below` fill only the portion to one side of the baseline. Note that in moving from one data point to the next, both `steps` and `fillsteps` first trace the change in x coordinate and then the change in y coordinate. See `steps`. 2 fsteps ?plotting styles fsteps ?style fsteps ?with fsteps ?fsteps Ffigure_fsteps The `fsteps` style is only relevant to 2D plotting. It connects consecutive points with two line segments: the first from (x1,y1) to (x1,y2) and the second from (x1,y2) to (x2,y2). The input column requires are the same as for plot styles `lines` and `points`. The difference between `fsteps` and `steps` is that `fsteps` traces first the change in y and then the change in x. `steps` traces first the change in x and then the change in y. See also ^ steps demo. ^ 2 histeps ?plotting styles histeps ?style histeps ?with histeps ?histeps Ffigure_histeps The `histeps` style is only relevant to 2D plotting. It is intended for plotting histograms. Y-values are assumed to be centered at the x-values; the point at x1 is represented as a horizontal line from ((x0+x1)/2,y1) to ((x1+x2)/2,y1). The lines representing the end points are extended so that the step is centered on at x. Adjacent points are connected by a vertical line at their average x, that is, from ((x1+x2)/2,y1) to ((x1+x2)/2,y2). The input column requires are the same as for plot styles `lines` and `points`. If `autoscale` is in effect, it selects the xrange from the data rather than the steps, so the end points will appear only half as wide as the others. See also ^ steps demo. ^ #TeX \newpage 2 heatmaps ?heatmaps Several of gnuplot's plot styles can be used to create heat maps. The choice of which style to use is dictated by the type of data. Ffigure_heatmap Pixel-based heat maps all have the property that each pixel in the map corresponds exactly to one original data value. The pixel-based image styles require a regular rectangular grid of data values; see `with image`. However it is possible to handle missing grid values (see `sparse`) and it is also possible to mask out only a portion of the grid for display (see `masking`). Unless there are a large number of grid elements, it is usually good to render each rectangular element separately (`with image pixels`) so that smoothing or lossy compression is not applied to the resulting "image". Ffigure_sector_heatmap A polar equivalent to image pixel-based heat maps can be generated using 2D plot style `sectors`. Each input point corresponds to exactly one annular sector of a polar grid, equivalent to a pixel. Unlike the polar grid surface option described below, any number of individual grid sectors may be provided. This plot style can be used in either polar or cartesian coordinate plots to place polar sectors anywhere on the graph. The figure here shows two halves of a polar heat map displaced across the origin by +/- Î”x on a cartesian coordinate plot. See `with sectors`. Ffigure_mask If the data points do not constitute a regular rectangular grid, they can often be used to fit a gridded surface by interpolation or by splines. Alternatively a point-density function can be mapped onto a gridded plane or smooth surface. See `set dgrid3d`. The gridded surface can then be plotted as a pm3d surface (see `masking` example). In this case the points on the heat map do not retain a one-to-one correspondence with the input data. I.e. the validity of the heat map represenation is only as good as the gridded approximation. The demo collection has examples of generating 2D heatmaps from a set of points ^ heatmap_points.dem ^ Ffigure_polar_grid If your copy of gnuplot was built with the --enable-polar-grid option, polar coordinate data points can be used to generate a 2D polar heat map in which each "pixel" corresponded to a pre-determined range of theta and r. See `set polar grid` and `with surface`. This process is exactly analogous to the use of `set dgrid3d` and `with pm3d` except that it operates in 2D polar coordinate space. 2 histograms ?style histograms ?with histograms ?set style histogram ?plotting styles histograms ?histograms The `histograms` style is only relevant to 2D plotting. It produces a bar chart from a sequence of parallel data columns. Each element of the `plot` command must specify a single input data source (e.g. one column of the input file), possibly with associated tic values or key titles. Four styles of histogram layout are currently supported. set style histogram clustered {gap } set style histogram errorbars {gap } {} set style histogram rowstacked set style histogram columnstacked set style histogram {title font "name,size" tc } The default style corresponds to `set style histogram clustered gap 2`. In this style, each set of parallel data values is collected into a group of boxes clustered at the x-axis coordinate corresponding to their sequential position (row #) in the selected datafile columns. Thus if datacolumns are selected, the first cluster is centered about x=1, and contains boxes whose heights are taken from the first entry in the corresponding data columns. This is followed by a gap and then a second cluster of boxes centered about x=2 corresponding to the second entry in the respective data columns, and so on. The default gap width of 2 indicates that the empty space between clusters is equivalent to the width of 2 boxes. All boxes derived from any one column are given the same fill color and/or pattern; however see the subsection `histograms colors`. Each cluster of boxes is derived from a single row of the input data file. It is common in such input files that the first element of each row is a label. Labels from this column may be placed along the x-axis underneath the appropriate cluster of boxes with the `xticlabels` option to `using`. The `errorbars` style is very similar to the `clustered` style, except that it requires additional columns of input for each entry. The first column holds the height (y value) of that box, exactly as for the `clustered` style. 2 columns: y yerr bar extends from y-yerr to y+err 3 columns: y ymin ymax bar extends from ymin to ymax The appearance of the error bars is controlled by the current value of `set errorbars` and by the optional specification. Two styles of stacked histogram are supported, chosen by the command `set style histogram {rowstacked|columnstacked}`. In these styles the data values from the selected columns are collected into stacks of boxes. Positive values stack upwards from y=0; negative values stack downwards. Mixed positive and negative values will produce both an upward stack and a downward stack. The default stacking mode is `rowstacked`. The `rowstacked` style places a box resting on the x-axis for each data value in the first selected column; the first data value results in a box a x=1, the second at x=2, and so on. Boxes corresponding to the second and subsequent data columns are layered on top of these, resulting in a stack of boxes at x=1 representing the first data value from each column, a stack of boxes at x=2 representing the second data value from each column, and so on. All boxes derived from any one column are given the same fill color and/or pattern (see `set style fill`). The `columnstacked` style is similar, except that each stack of boxes is built up from a single data column. Each data value from the first specified data column yields a box in the stack at x=1, each data value from the second specified data column yields a box in the stack at x=2, and so on. In this style the color of each box is taken from the row number, rather than the column number, of the corresponding data field. Box widths may be modified using the `set boxwidth` command. Box fill styles may be set using the `set style fill` command. Histograms always use the x1 axis, but may use either y1 or y2. If a plot contains both histograms and other plot styles, the non-histogram plot elements may use either the x1 or the x2 axis. One additional style option `set style histogram nokeyseparators` is relevant only to plots that contain multiple histograms. See `newhistogram` for additional discussion of this case. Examples: Ffigure_histclust Suppose that the input file contains data values in columns 2, 4, 6, ... and error estimates in columns 3, 5, 7, ... This example plots the values in columns 2 and 4 as a histogram of clustered boxes (the default style). Because we use iteration in the plot command, any number of data columns can be handled in a single command. See `plot for`. set boxwidth 0.9 relative set style data histograms set style histogram cluster set style fill solid 1.0 border lt -1 plot for [COL=2:4:2] 'file.dat' using COL This will produce a plot with clusters of two boxes (vertical bars) centered at each integral value on the x axis. If the first column of the input file contains labels, they may be placed along the x-axis using the variant command plot for [COL=2:4:2] 'file.dat' using COL:xticlabels(1) Ffigure_histerrorbar If the file contains both magnitude and range information for each value, then error bars can be added to the plot. The following commands will add error bars extending from (y-) to (y+), capped by horizontal bar ends drawn the same width as the box itself. The error bars and bar ends are drawn with linewidth 2, using the border linetype from the current fill style. set errorbars fullwidth set style fill solid 1 border lt -1 set style histogram errorbars gap 2 lw 2 plot for [COL=2:4:2] 'file.dat' using COL:COL+1 This shows how to plot the same data as a rowstacked histogram. Just to be different, the plot command in this example lists the separate columns individually rather than using iteration. set style histogram rowstacked plot 'file.dat' using 2, '' using 4:xtic(1) Ffigure_histrows This will produce a plot in which each vertical bar corresponds to one row of data. Each vertical bar contains a stack of two segments, corresponding in height to the values found in columns 2 and 4 of the datafile. #TeX \vspace{1em} Finally, the commands set style histogram columnstacked plot 'file.dat' using 2, '' using 4 Ffigure_histcols will produce two vertical stacks, one for each column of data. The stack at x=1 will contain a box for each entry in column 2 of the datafile. The stack at x=2 will contain a box for each parallel entry in column 4 of the datafile. Because this interchanges gnuplot's usual interpretation of input rows and columns, the specification of key titles and x-axis tic labels must also be modified accordingly. See the comments given below. set style histogram columnstacked plot '' u 5:key(1) # uses first column to generate key titles plot '' u 5 title columnhead # uses first row to generate xtic labels Note that the two examples just given present exactly the same data values, but in different formats. 3 newhistogram ?newhistogram ?with histograms newhistogram ?histograms newhistogram ?styles histograms newhistogram ?plotting styles histograms newhistogram Syntax: newhistogram {"" {font "name,size"} {tc <colorspec>}} {lt <linetype>} {fs <fillstyle>} {at <x-coord>} More than one set of histograms can appear in a single plot. In this case you can force a gap between them, and a separate label for each set, by using the `newhistogram` command. For example set style histogram cluster plot newhistogram "Set A", 'a' using 1, '' using 2, '' using 3, \ newhistogram "Set B", 'b' using 1, '' using 2, '' using 3 The labels "Set A" and "Set B" will appear beneath the respective sets of histograms, under the overall x axis label. The newhistogram command can also be used to force histogram coloring to begin with a specific color (linetype). By default colors will continue to increment successively even across histogram boundaries. Here is an example using the same coloring for multiple histograms plot newhistogram "Set A" lt 4, 'a' using 1, '' using 2, '' using 3, \ newhistogram "Set B" lt 4, 'b' using 1, '' using 2, '' using 3 Similarly you can force the next histogram to begin with a specified fillstyle. If the fillstyle is set to `pattern`, then the pattern used for filling will be incremented automatically. Starting a new histogram will normally add a blank entry to the key, so that titles from this set of histogram components will be separated from those of the previous histogram. This blank line may be undesirable if the components have no individual titles. It can be suppressed by modifying the style with `set style histogram nokeyseparators`. Ffigure_newhist The `at <x-coord>` option sets the x coordinate position of the following histogram to <x-coord>. For example set style histogram cluster set style data histogram set style fill solid 1.0 border -1 set xtic 1 offset character 0,0.3 plot newhistogram "Set A", \ 'file.dat' u 1 t 1, '' u 2 t 2, \ newhistogram "Set B" at 8, \ 'file.dat' u 2 t 2, '' u 2 t 2 will position the second histogram to start at x=8. 3 automated iteration over multiple columns ?automated ?with histograms automated ?histograms automated ?styles histograms automated ?plotting styles histograms automated If you want to create a histogram from many columns of data in a single file, it is very convenient to use the plot iteration feature. See `plot for`. For example, to create stacked histograms of the data in columns 3 through 8 set style histogram columnstacked plot for [i=3:8] "datafile" using i title columnhead 3 histogram color assignments ?with histograms colors ?histograms colors ?styles histograms colors ?plotting styles histograms colors The program assigns a color to each component box in a histogram automatically such that equivalent data values maintain a consistent color wherever they appear in the rows or columns of the histogram. The colors are taken from successive linetypes, starting either with the next unused linetype or an initial linetype provided in a `newhistogram` element. In some cases this mechanism fails due to data sources that are not truly parallel (i.e. some files contain incomplete data). In other cases there may be additional properties of the data that could be visualized by, say, varying the intensity or saturation of their base color. As an alternative to the automatic color assignment, you can provide an explicit color value for each data value in a second `using` column via the `linecolor variable` or `rgb variable` mechanism. See `colorspec`. Depending on the layout of your data, the color category might correspond to a row header or a column header or a data column. Note that you will probably have to customize the key sample colors to match (see `keyentry`). Example: Suppose file_001.dat through file_008.dat contain one column with a category identifier A, B, C, ... and a second column with a data value. Not all of the files contain a line for every category, so they are not truly parallel. The program would be wrong to assign the same color to the value from line N in each file. Instead we assign a color based on the category in column 1. file(i) = sprintf("file_%03d.dat",i) array Category = ["A", "B", "C", "D", "E", "F"] color(c) = index(Category, strcol(c)) set style data histogram plot for [i=1:8] file(i) using 2:(color(1)) linecolor variable A more complete example including generation of a custom key is in the demo collection ^ <a href="https://www.apklas.com?arsae=http%3A%2F%2Fwww.gnuplot.info%2Fdemo%2Fhistogram_colors.html" target="_parent"> histogram_colors.dem ^ </a> D histogram_colors 1 2 hsteps ?plotting styles hsteps ?style hsteps ?with hsteps ?hsteps The 2D plotting style `with hsteps` renders a horizontal line segment ("step") for each data point. The step may extend to the left, to the right, or to both sides of the point's x-coordinate. Additional keywords control the lines connecting adjacent steps and option area fill between the step and a baseline y value. Syntax: plot <data> with hsteps {forward|backward} {baseline|pillars|link|nolink} {{above|below} y=<baseline>} {offset <y-offset>} 2 columns: x y 3 columns: x y width This plot style requires 2 or 3 columns of data. Additional input columns can be used to provide variable line or fill colors (see `rgbcolor variable`). The x values of the input data are assumed to be monotonic. If the width of each step is not explicitly given through a third input column, each segmentâ€™s width is calculated so that it abuts the adjacent horizontal segments. A negative value in column 3 will be treated as a request for a full-width step. The `forward` and `backward` keywords can be used to specify the direction in which the horizontal segment extends from the given x coordinate. If neither is specified, the horizontal segment extends on both sides of the given x-value halfway to the x-value of the next adjacent point. However, for the first and last points, where there are no corresponding outer adjacent points, the horizontal segments are extrapolated using distances to the adjacent inner points (see `histeps`, `boxes`). The default (`baseline`) and `pillar` variants employ a baseline y value. If not provided in the plot command, the baseline is taken to be y=0. If the plot command uses a fill style, the baseline also serves to delimit one boundary of the fill area. Four style variants are possible. Ffigure_hsteps_baseline `baseline` (default): If there is no gap along x between adjacent steps, they are connected by a vertical line segment between them. This produces a curve like the `steps`, `histeps`, or `fsteps` styles. If there is a gap between steps, usually because the width is less than the point spacing, the connecting line drops to the baseline and continues along it before rising again. This produces a sequence of rectangular pulses. set xzeroaxis plot $data using 1:2 with hsteps plot $data using 1:2:(0.5) with hsteps Ffigure_hsteps_pillar `pillar`: At each end of each step a vertical line is drawn to the baseline. Note that no horizontal line segments are drawn at the baseline. plot $data using 1:2 with hsteps pillar plot $data using 1:2:(0.5) with hsteps pillar plot $data using 1:2:(0.5) \ with hsteps pillar above fc "blue", \ $data using 1:2:(0.5) \ with hsteps pillar below fc "red" #TeX \vspace{6ex} Ffigure_hsteps_nolink `nolink`: No connecting line is drawn between adjacent steps. Baseline and fill properties are not relevant to this variant. plot $data using 1:2 with hsteps nolink, \ $data using 1:2 with hsteps nolink forward, \ $data using 1:2 with hsteps nolink backward, \ $data using 1:2 with points pt "|" #TeX \vspace{9ex} Ffigure_hsteps_link `link`: Adjacent steps steps are connected by a single straight line segment. Depending on the step widths, this line may be diagonal rather than vertical. Example: The `link` variant can be superimposed onto the `pillar` variant to produce a stacked histogram plot in which category boundaries are connected. set style line 11 lw 2 lc "gray" dt "." set style line 12 lw 2 lc variable plot $data using 1:3:(0.5) ls 11 with hsteps link, \ $data using 1:3:(0.5):1 ls 12 with hsteps pillar fs solid 0.7 border, \ $data using 1:4:(0.5) ls 11 with hsteps link, \ $data using 1:4:(0.5):1 ls 12 with hsteps pillar fs transparent pattern 1 border 3 offset Ffigure_hsteps_offset ?with hsteps offset ?hsteps offset The offset value modifies any of the `with hsteps` variants by adding an increment to the y value of both the data point itself (column 2) and the baseline of the plot it appears in. An example of use is to draw a logic circuit timing chart in which pulse waveforms are aligned vertically. In general the offset can be used to stack plots from multiple data sets that share a common range of y values. # bit(k,char) is a function that returns 0 or 1 # for the state of bit k in an ASCII character set style fill solid 0.2 border plot for [k=1:8] STR using 1:(bit(k,STR[$1])):(0.5) \ with hsteps fillcolor "black" offset k 3 missing data ?with hsteps missing-data ?hsteps missing-data In the hsteps style, empty lines, NaN values, and missing data have distinct meanings. If an empty line is present in the data, the data series is reset at that point. This is analogous to a blank line causing a break to start a new curve in the case of `with lines`. If an x-value contains NaN, it is processed in the same manner as an empty line. If the x-value is valid but the y-value contains NaN, no horizontal line is drawn for that particular data point but the x-value is still used if needed to estimate the step width. 2 image ?plotting styles image ?style image ?with image ?image ?rgbimage ?rgbalpha The `image`, `rgbimage`, and `rgbalpha` plotting styles all project a uniformly sampled grid of data values onto a plane in either 2D or 3D. The input data may be an actual bitmapped image, perhaps converted from a standard format such as PNG, or a simple array of numerical values. These plot styles are often used to produce heatmaps. For 2D heatmaps in polar coordinates, see `set polar grid`. Ffigure_heatmap This figure illustrates generation of a heat map from an array of scalar values. The current palette is used to map each value onto the color assigned to the corresponding pixel. See also `sparse`. plot '-' matrix with image 5 4 3 1 0 2 2 0 0 1 0 0 0 1 0 0 1 2 4 3 e e Ffigure_rgb3D Each pixel (data point) of the input 2D image will become a rectangle or parallelepiped in the plot. The coordinates of each data point will determine the center of the parallelepiped. That is, an M x N set of data will form an image with M x N pixels. This is different from the pm3d plotting style, where an M x N set of data will form a surface of (M-1) x (N-1) elements. The scan directions for a binary image data grid can be further controlled by additional keywords. See `binary keywords flipx`, `keywords center`, and `keywords rotate`. Ffigure_scaled_image Image data can be scaled to fill a particular rectangle within a 2D plot coordinate system by specifying the x and y extent of each pixel. See `binary keywords dx` and `dy`. To generate the figure at the right, the same input image was placed multiple times, each with a specified dx, dy, and origin. The input PNG image of a building is 50x128 pixels. The tall building was drawn by mapping this using `dx=0.5 dy=1.5`. The short building used a mapping `dx=0.5 dy=0.35`. The `image` style handles input pixels containing a grayscale or color palette value. Thus 2D plots (`plot` command) require 3 columns of data (x,y,value), while 3D plots (`splot` command) require 4 columns of data (x,y,z,value). The `rgbimage` style handles input pixels that are described by three separate values for the red, green, and blue components. Thus 5D data (x,y,r,g,b) is needed for `plot` and 6D data (x,y,z,r,g,b) for `splot`. The individual red, green, and blue components are assumed to lie in the range [0:255]. This matches the convention used in PNG and JPEG files (see `binary filetype`). However some data files use an alternative convention in which RGB components are floating point values in the range [0:1]. To use the `rgbimage` style with such data, first use the command `set rgbmax 1.0`. =alpha channel The `rgbalpha` style handles input pixels that contain alpha channel (transparency) information in addition to the red, green, and blue components. Thus 6D data (x,y,r,g,b,a) is needed for `plot` and 7D data (x,y,z,r,g,b,a) for `splot`. The r, g, b, and alpha components are assumed to lie in the range [0:255]. To plot data for which RGBA components are floating point values in the range [0:1], first use the command `set rgbmax 1.0`. If only a single data column is provided for the color components of either rgbimage or rgbalpha plots, it is interpreted as containing 32 bit packed ARGB data using the convention that alpha=0 means opaque and alpha=255 means fully transparent. Note that this is backwards from the alpha convention if alpha is supplied in a separate column, but matches the ARGB packing convention for individual commands to set color. See `colorspec`. 3 transparency ?image transparency ?transparency ?alpha channel The `rgbalpha` plotting style assumes that each pixel of input data contains an alpha value in the range [0:255]. A pixel with alpha = 0 is purely transparent and does not alter the underlying contents of the plot. A pixel with alpha = 255 is purely opaque. All terminal types can handle these two extreme cases. A pixel with 0 < alpha < 255 is partially transparent. Terminal types that do not support partial transparency will round this value to 0 or 255. D argb_hexdata 2 3 image pixels ?plotting styles image pixels ?style image pixels ?with image pixels ?image pixels ?pixels =heatmaps Some terminals use device- or library-specific optimizations to render image data within a rectangular 2D area. This sometimes produces undesirable output, e.g. inter-pixel smoothing, bad clipping or missing edges. An example of this is the smoothing applied by web browsers when rendering svg images. The `pixels` keyword tells gnuplot to use generic code to render the image pixel-by-pixel. This rendering mode is slower and may result in larger output files, but should produce a consistent rendered view on all terminals. It may in particular be preferable for heatmaps with a small number of pixels. Example: plot 'data' with image pixels 2 impulses ?plotting styles impulses ?style impulses ?with impulses ?impulses Ffigure_impulses The `impulses` style displays a vertical line from y=0 to the y value of each point (2D) or from z=0 to the z value of each point (3D). Note that the y or z values may be negative. Data from additional columns can be used to control the color of each impulse. To use this style effectively in 3D plots, it is useful to choose thick lines (linewidth > 1). This approximates a 3D bar chart. 1 column: y 2 columns: x y # line from [x,0] to [x,y] (2D) 3 columns: x y z # line from [x,y,0] to [x,y,z] (3D) 2 labels ?plotting styles labels ?style labels ?with labels ?labels Ffigure_labels1 The `labels` style reads coordinates and text from a data file and places the text string at the corresponding 2D or 3D position. 3 or 4 input columns of basic data are required. Additional input columns may be used to provide properties that vary point by point such as text rotation angle (keywords `rotate variable`) or color (see `textcolor variable`). 3 columns: x y string # 2D version 4 columns: x y z string # 3D version The font, color, rotation angle and other properties of the printed text may be specified as additional command options (see `set label`). The example below generates a 2D plot with text labels constructed from the city whose name is taken from column 1 of the input file, and whose geographic coordinates are in columns 4 and 5. The font size is calculated from the value in column 3, in this case the population. CityName(String,Size) = sprintf("{/=%d %s}", Scale(Size), String) plot 'cities.dat' using 5:4:(CityName(stringcolumn(1),$3)) with labels If we did not want to adjust the font size to a different size for each city name, the command would be much simpler: plot 'cities.dat' using 5:4:1 with labels font "Times,8" If the labels are marked as `hypertext` then the text only appears if the mouse is hovering over the corresponding anchor point. See `hypertext`. In this case you must enable the label's `point` attribute so that there is a point to act as the hypertext anchor: plot 'cities.dat' using 5:4:1 with labels hypertext point pt 7 Ffigure_labels2 The `labels` style can also be used in place of the `points` style when the set of predefined point symbols is not suitable or not sufficiently flexible. For example, here we define a set of chosen single-character symbols and assign one of them to each point in a plot based on the value in data column 3: set encoding utf8 symbol(z) = "âˆ™â–¡+âŠ™â™ â™£â™¡â™¢"[int(z):int(z)] splot 'file' using 1:2:(symbol($3)) with labels This example shows use of labels with variable rotation angle in column 4 and textcolor ("tc") in column 5. Note that variable color is always taken from the last column in the `using` specifier. plot $Data using 1:2:3:4:5 with labels tc variable rotate variable 2 lines ?plotting styles lines ?style lines ?with lines ?lines Ffigure_lines The `lines` style connects adjacent points with straight line segments. It may be used in either 2D or 3D plots. The basic form requires 1, 2, or 3 columns of input data. Additional input columns may be used to provide information such as variable line color (see `rgbcolor variable`). 2D form (no "using" spec) 1 column: y # implicit x from row number 2 columns: x y 3D form (no "using" spec) 1 column: z # implicit x from row, y from index 3 columns: x y z See also `linetypes`, `linewidth`, and `linestyle`. 2 linespoints ?plotting styles linespoints ?style linespoints ?with linespoints ?style lp ?with lp ?linespoints ?lp ?pointinterval ?pointnumber Ffigure_linespoints The `linespoints` style (short form `lp`) connects adjacent points with straight line segments and then goes back to draw a small symbol at each point. Points are drawn with the default size determined by `set pointsize` unless a specific point size is given in the plot command or a variable point size is provided in an additional column of input data. Additional input columns may also be used to provide information such as variable line color. See `lines` and `points`. Two keywords control whether or not every point in the plot is marked with a symbol, `pointinterval` (short form `pi`) and `pointnumber` (short form `pn`). `pi N` or `pi -N` tells gnuplot to only place a symbol on every Nth point. A negative value for N will erase the portion of line segment that passes underneath the symbol. The size of the erased portion is controlled by `set pointintervalbox`. `pn N` or `pn -N` tells gnuplot to label only N of the data points, evenly spaced over the data set. As with `pi`, a negative value for N will erase the portion of line segment that passes underneath the symbol. 2 masking ?plotting styles mask ?plot with mask ?with mask ?masking The plotting style `with mask` is used to define a masking region that can be applied to pm3d surfaces or to images specified later in the same `plot` or `splot` command. Input data is interpreted as a stream of [x,y] or [x,y,z] coordinates defining the vertices of one or more polygons. As in plotting style `with polygons`, polygons are separated by a blank line. If the mask is part of a 3D (splot) command then a column of z values is required on input but is currently not used for anything. If a mask definition is present in the plot command, then any subsequent image or pm3d surface in the same command can be masked by adding the keyword `mask`. If no mask has been defined, this keyword is ignored. This example illustrates using the convex hull circumscribing a set of points to mask the corresponding region of a pm3d surface. Ffigure_mask ^<p align="center"><picture> ^ <source srcset="figure_mask.webp" type="image/webp"> ^ <img src="figure_mask.png" alt="figure_mask"> ^ </source></picture></p><p> set table $HULL plot $POINTS using 1:2 convexhull unset table set view map set multiplot layout 1,2 splot $POINTS using 1:2:3 with pm3d, \ $POINTS using 1:2:(0) nogrid with points splot $HULL using 1:2:(0) with mask, \ $POINTS using 1:2:3 mask with pm3d unset multiplot The `splot` command for the first panel renders the unmasked surface created by dgrid3d from the original points and then the points themselves, in that order. The `splot` command for the second panel renders the masked surface. Note that definition of the mask must come first (plot `with mask`), followed by the pm3d surface it applies to (plot style `with pm3d` modified by the `mask` keyword). A more complete version of this example is in the demo collection ^ <a href="https://www.apklas.com?arsae=http%3A%2F%2Fwww.gnuplot.info%2Fdemo%2Fmask_pm3d.html" target="_parent"> mask_pm3d.dem ^ </a> Although it is not shown here, a single mask can include multiple polygonal regions. The masking commands are EXPERIMENTAL. Details may change in a future release. 2 parallelaxes Ffigure_parallel ?plotting styles parallelaxes ?plot with parallelaxes ?with parallelaxes ?parallelaxes ?parallel Parallel axis plots can highlight correlation in a multidimensional data set. Individual columns of input data are each associated with a separately scaled vertical axis. If all columns are drawn from a single file then each line on the plot represents values from a single row of data in that file. It is common to use some discrete categorization to assign line colors, allowing visual exploration of the correlation between this categorization and the axis dimensions. Syntax: set style data parallelaxes plot $DATA using col1{:varcol1} {at <xpos>} {<line properties using col2 ... change: version of gnuplot introduced a change in the syntax for plot style parallelaxes. revised allows an unlimited number parallel axes. with parallelaxes col new also explicit placement vertical axes along x axis as example below. if no coordinate is provide n will be placed at array xpos by default automatically determine range and scale individual from input data but usual commands can used to customize this. see paxis polar plots="polar" ffigure_polar are generated changing current system before issuing command. option tells interpret coordinates>,<radius> rather than <x>,<y>. Many, but not all, of the 2D plotting styles work in polar mode. The figure shows a combination of plot styles `lines` and `filledcurves`. See `set polar`, `set rrange`, `set size square`, `set theta`, `set ttics`. ?polar heatmap Polar heatmaps can be generated using plot style `with surface` together with `set polar grid`. Ffigure_polar_grid set size square set angle degrees set rtics set grid polar set palette cubehelix negative gamma 0.8 set polar grid gauss kdensity scale 35 set polar grid theta [0:190] plot DATA with surface, DATA with points pt 7 2 points ?plotting styles points ?style points ?with points ?points ?point type ?pointtype Ffigure_points The `points` style displays a small symbol at each point. The command `set pointsize` may be used to change the default size of all points. The point type defaults to that of the linetype. See `linetypes`. If no `using` spec is found in the plot command, input data columns are interpreted implicitly in the order x y pointsize pointtype color Any columns beyond the first two (x and y) are optional; they correspond to additional plot properties `pointsize variable`, `pointtype variable`, etc. The first 8 point types are shared by all terminals. Individual terminals may provide a much larger number of distinct point types. Use the `test` command to show what is provided by the current terminal settings. Alternatively any single printable character may be given instead of a numerical point type, as in the example below. You may use any unicode character as the pointtype (assumes utf8 support). See `escape sequences`. Longer strings may be plotted using plot style `labels` rather than `points`. plot f(x) with points pt "#" plot d(x) with points pt "\U+2299" ?points variable ?with points variable =variable ?variable ?pointtype variable ?pointsize variable When using the keywords `pointtype`, `pointsize`, or `linecolor` in a plot command, the additional keyword `variable` may be given instead of a number. In this case the corresponding properties of each point are assigned by additional columns of input data. Variable pointsize is always taken from the first additional column provided in a `using` spec. Variable color is always taken from the last additional column. See `colorspec`. If all three properties are specified for each point, the order of input data columns is thus plot DATA using x:y:pointsize:pointtype:color \ with points lc variable pt variable ps variable Note: for information on user-defined program variables, see `variables`. 2 polygons ?plotting styles polygons ?style polygons ?with polygons ?polygons 2D plots: plot DATA {using 1:2} with polygons `plot with polygons` is currently treated as `plot with filledcurves closed`. Each polygon may be assigned a separate color by providing a third using specifier and the keywords `lc variable` (value is interpreted as a linetype) or `lc rgb variable` (value is interpreted as a 24-bit RGB color). Only the color value from the first vertex of the polygon is used. The border line type, if any, is taken from the fill style. 3D plots: splot DATA {using x:y:z} with polygons {fillstyle <fillstyle spec>} {fillcolor <colorspec>} `splot with polygons` uses pm3d to render individual triangles, quadrangles, and larger polygons in 3D. These may be facets of a 3D surface or isolated shapes. The code assumes that the vertices lie in a plane. Vertices defining individual polygons are read from successive records of the input file. A blank line separates one polygon from the next. The fill style and color may be specified in the splot command, otherwise the global fillstyle from `set style fill` is used. Due to limitations in the pm3d code, a single border line style from `set pm3d border` is applied to all 3D polygons. This restriction may be removed in a later gnuplot version. Each polygon may be assigned a separate RGB color by providing a fourth using specifier and the keywords `lc variable` (value is interpreted as a linetype) or `lc rgb variable` (value is interpreted as a 24-bit RGB color). Only the color value from the first vertex of the polygon is used. pm3d sort order and lighting are applied to the faces. It is probably always desirable to use `set pm3d depthorder`. Ffigure_polygons set xyplane at 0 set view equal xyz unset border unset tics set pm3d depth set pm3d border lc "black" lw 1.5 splot 'icosahedron.dat' with polygons \ fs transparent solid 0.8 fc bgnd 2 rgbalpha ?plotting styles rgbalpha ?style rgbalpha ?with rgbalpha See `image`. 2 rgbimage ?plotting styles rgbimage ?style rgbimage ?with rgbimage See `image`. 2 sectors ?plotting styles sectors ?with sectors ?sectors ?windrose Ffigure_sector_definition The 2D plotting style `with sectors` renders one annular segment ("sector") for each line of input data. The shape of each sector is described by four required data values. An additional pair of data values can be included to specify the origin of the annulus this sector is taken from. A per-sector color may be provided in an additional column. The plot style itself can be used in either cartesian or polar mode (`set polar`). The units and interpretation for the azimuth and the sector angle are controlled using `set angles` and `set theta`. Columns 1 and 2 specify the azimuth (theta) and radius (r) of one corner of the sector. #TeX \newline Columns 3 and 4 specify the angular and radial extents of the sector ("sector_angle" and "annular_width"). #TeX \newline Columns 5 and 6, if present, specify the coordinates of the center of the annulus (default [0,0]). The interpretation is [x,y] in cartesian mode and [theta,r] in polar mode. Syntax: plot DATA {using specifier} {units xy | units xx | units yy} using specifier 4 columns: azimuth radius sector_angle annular_width 5 columns: azimuth radius sector_angle annular_width color 6 columnd: azimuth radius sector_angle annular_width center_x center_y 7 columns: azimuth radius sector_angle annular_width center_x center_y color Note that if the x and y axis scales are not equal, the envelope of the full annulus in x/y coordinates will appear as an ellipse rather than a circle. The annulus envelope and thus the apparent sector annular width can be adjusted to correct for unequal axis scales using the same mechanism as for ellipses. Adding `units xx` to the command line causes the sector to be rendered as if the current x axis scale applied equally to both x and y. Similarly `units yy` causes the sector to be rendered as if the current y axis scale applied equally to both x and y. See `set isotropic`, `set style ellipse`. Ffigure_windrose Plotting with sectors can provide polar coordinate equivalents for the cartesian plot styles `boxes` (see wind rose figure), `boxxyerror` and `image pixels` (see example in `heatmaps`). Because sector plots are compatible with cartesian mode plot layout, multiple plots can be placed at different places on a single graph, which would not be possible for other polar mode plot styles. An example of using sectors to create a wind rose in shown here. Other applications include polar heatmaps, dial charts, pie/donut charts, and annular error boxes for data points in polar coordinates. Worked examples for all of these are given in the ^ <a href="https://www.apklas.com?arsae=http%3A%2F%2Fwww.gnuplot.info%2Fdemo%2Fsectors.html" target="_parent"> sectors demo. ^ </a> 2 spiderplot ?plotting styles spiderplot ?with spiderplot ?spiderplot ?radar chart Spider plots are essentially parallel axis plots in which the axes are arranged radially rather than vertically. Such plots are sometimes called `radar charts`. In gnuplot this requires working within a coordinate system established by the command `set spiderplot`, analogous to `set polar` except that the angular coordinate is determined implicitly by the parallel axis number. The appearance, labelling, and tic placement of the axes is controlled by `set paxis`. Further style choices are controlled using `set style spiderplot`, `set grid`, and the individual components of the plot command. Because each spider plot corresponds to a row of data rather than a column, it would make no sense to generate key entry titles in the normal way. Instead, if a plot component contains a title the text is used to label the corresponding axis. This overrides any previous `set paxis n label "Foo"`. To place a title in the key, you can either use a separate `keyentry` command or extract text from a column in the input file with the `key(column)` using specifier. See `keyentry`, `using key`. In this figure a spiderplot with 5 axes is used to compare multiple entities that are each characterized by five scores. Each line (row) in $DATA generates a new polygon on the plot. Ffigure_spiderplot $DATA << EOD A B C D E F George 15 75 20 43 90 50 Harriet 40 40 40 60 30 50 EOD set spiderplot set style spiderplot fs transparent solid 0.2 border set for [p=1:5] paxis p range [0:100] set for [p=2:5] paxis p tics format "" set paxis 1 tics font ",9" set for [p=1:5] paxis p label sprintf("Score %d",p) set grid spiderplot plot for [i=1:5] $DATA using i:key(1) 3 newspiderplot ?newspiderplot ?spiderplot newspiderplot Normally the sequential elements of a plot command `with spiderplot` each correspond to one vertex of a single polygon. In order to describe multiple polygons in the same plot command, they must be separated by `newspiderplot`. Example: # One polygon with 10 vertices plot for [i=1:5] 'A' using i, for [j=1:5] 'B' using j # Two polygons with 5 vertices plot for [i=1:5] 'A' using i, newspiderplot, for [j=1:5] 'B' using j 2 steps ?plotting styles steps ?style steps ?with steps ?steps Ffigure_steps The `steps` style is only relevant to 2D plotting. It connects consecutive points with two line segments: the first from (x1,y1) to (x2,y1) and the second from (x2,y1) to (x2,y2). The input column requires are the same as for plot styles `lines` and `points`. The difference between `fsteps` and `steps` is that `fsteps` traces first the change in y and then the change in x. `steps` traces first the change in x and then the change in y. To fill the area between the curve and the baseline at y=0, use `fillsteps`. See also ^ <a href="https://www.apklas.com?arsae=http%3A%2F%2Fwww.gnuplot.info%2Fdemo%2Fsteps.html" target="_parent"> steps demo. ^ </a> 2 surface ?plotting styles surface ?style surface ?with surface The plot style `with surface` has two uses. In 3D plots, `with surface` always produces a surface. If a 3D data set is recognizable as a mesh (grid) then by default the program implicitly treats the plot style `with lines` as requesting a gridded surface, making `with lines` a synonym for `with surface`. However the command `set surface explicit` suppresses this treatment, in which case `with surface` and `with lines` become distinct styles that may be used in the same plot. If you have points in 3D that are not recognized as a grid, you may be able to fit a suitable grid first. See `set dgrid3d`. In 2D polar mode plots, `with surface` is used to produce a solid fill gridded represention of the data. Generation of the surface is controlled using the command `set polar grid`. 2 vectors ?plotting styles vectors ?style vectors ?with vectors ?vectors Ffigure_vectors The 2D `vectors` style draws a vector from (x,y) to (x+xdelta,y+ydelta). The 3D `vectors` style is similar, but requires six columns of basic data. In both cases, an additional input column (5th in 2D, 7th in 3D) may be used to provide variable (per-datapoint) color information. (see `linecolor` and `rgbcolor variable`). A small arrowhead is drawn at the end of each vector. 4 columns: x y xdelta ydelta 6 columns: x y z xdelta ydelta zdelta The keywords "with vectors" may be followed by inline arrow style properties, by reference to a predefined arrow style, or by a request to read the index of the desired arrow style for each vector from a separate input column. See the first three examples below. Examples: plot ... using 1:2:3:4 with vectors filled heads plot ... using 1:2:3:4 with vectors arrowstyle 3 plot ... using 1:2:3:4:5 with vectors arrowstyle variable splot 'file.dat' using 1:2:3:(1):(1):(1) with vectors filled head lw 2 Notes: You cannot mix the `arrowstyle` keyword with other line style qualifiers in the plot command. An additional column of color values is required if the arrow style includes `lc variable` or `lc rgb variable`. splot with vectors is supported only for `set mapping cartesian`. `set clip one` and `set clip two` affect vectors drawn in 2D. See `set clip` and `arrowstyle`. See also the 2D plot style `with arrows` that is identical to `with vectors` except that each arrow is specified using x:y:length:angle. #TeX \newpage 2 xerrorbars ?plotting styles xerrorbars ?style xerrorbars ?with xerrorbars ?xerrorbars Ffigure_xerrorbars The `xerrorbars` style is only relevant to 2D data plots. `xerrorbars` is like `points`, except that a horizontal error bar is also drawn. At each point (x,y), a line is drawn from (xlow,y) to (xhigh,y) or from (x-xdelta,y) to (x+xdelta,y), depending on how many data columns are provided. The appearance of the tic mark at the ends of the bar is controlled by `set errorbars`. The clearance between the point and the error bars is controlled by `set pointintervalbox`. The basic style requires either 3 or 4 columns: 3 columns: x y xdelta 4 columns: x y xlow xhigh An additional input column (4th or 5th) may be used to provide variable color. This style does not permit variable point properties. 2 xyerrorbars ?plotting styles xyerrorbars ?style xyerrorbars ?with xyerrorbars ?xyerrorbars Ffigure_xyerrorbars The `xyerrorbars` style is only relevant to 2D data plots. `xyerrorbars` is like `points`, except that horizontal and vertical error bars are also drawn. At each point (x,y), lines are drawn from (x,y-ydelta) to (x,y+ydelta) and from (x-xdelta,y) to (x+xdelta,y) or from (x,ylow) to (x,yhigh) and from (xlow,y) to (xhigh,y), depending upon the number of data columns provided. The appearance of the tic mark at the ends of the bar is controlled by `set errorbars`. The clearance between the point and the error bars is controlled by `set pointintervalbox`. Either 4 or 6 input columns are required. 4 columns: x y xdelta ydelta 6 columns: x y xlow xhigh ylow yhigh If data are provided in an unsupported mixed form, the `using` specifier of the `plot` command should be used to set up the appropriate form. For example, if the data are of the form (x,y,xdelta,ylow,yhigh), then you can use plot 'data' using 1:2:($1-$3):($1+$3):4:5 with xyerrorbars An additional input column (5th or 7th) may be used to provide variable color. This style does not permit variable point properties. #TeX \newpage 2 xerrorlines ?plotting styles xerrorlines ?style xerrorlines ?with xerrorlines ?xerrorlines Ffigure_xerrorlines The `xerrorlines` style is only relevant to 2D data plots. `xerrorlines` is like `linespoints`, except that a horizontal error line is also drawn. At each point (x,y), a line is drawn from (xlow,y) to (xhigh,y) or from (x-xdelta,y) to (x+xdelta,y), depending on how many data columns are provided. The appearance of the tic mark at the ends of the bar is controlled by `set errorbars`. The basic style requires either 3 or 4 columns: 3 columns: x y xdelta 4 columns: x y xlow xhigh An additional input column (4th or 5th) may be used to provide variable color. This style does not permit variable point properties. 2 xyerrorlines ?plotting styles xyerrorlines ?style xyerrorlines ?with xyerrorlines ?xyerrorlines Ffigure_xyerrorlines The `xyerrorlines` style is only relevant to 2D data plots. `xyerrorlines` is like `linespoints`, except that horizontal and vertical error bars are also drawn. At each point (x,y), lines are drawn from (x,y-ydelta) to (x,y+ydelta) and from (x-xdelta,y) to (x+xdelta,y) or from (x,ylow) to (x,yhigh) and from (xlow,y) to (xhigh,y), depending upon the number of data columns provided. The appearance of the tic mark at the ends of the bar is controlled by `set errorbars`. Either 4 or 6 input columns are required. 4 columns: x y xdelta ydelta 6 columns: x y xlow xhigh ylow yhigh If data are provided in an unsupported mixed form, the `using` specifier of the `plot` command should be used to set up the appropriate form. For example, if the data are of the form (x,y,xdelta,ylow,yhigh), then you can use plot 'data' using 1:2:($1-$3):($1+$3):4:5 with xyerrorlines An additional input column (5th or 7th) may be used to provide variable color. This style does not permit variable point properties. 2 yerrorbars ?plotting styles yerrorbars ?plotting styles errorbars ?style yerrorbars ?with yerrorbars ?style errorbars ?with errorbars ?yerrorbars =errorbars Ffigure_yerrorbars The `yerrorbars` (or `errorbars`) style is only relevant to 2D data plots. `yerrorbars` is like `points`, except that a vertical error bar is also drawn. At each point (x,y), a line is drawn from (x,y-ydelta) to (x,y+ydelta) or from (x,ylow) to (x,yhigh), depending on how many data columns are provided. The appearance of the tic mark at the ends of the bar is controlled by `set errorbars`. The clearance between the point and the error bars is controlled by `set pointintervalbox`. 2 columns: [implicit x] y ydelta 3 columns: x y ydelta 4 columns: x y ylow yhigh Additional input columns may be used to provide information such as variable point size, point type, or color. See also ^ <a href="https://www.apklas.com?arsae=http%3A%2F%2Fwww.gnuplot.info%2Fdemo%2Fmgr.html" target="_parent"> errorbar demo. ^ </a> 2 yerrorlines ?plotting styles yerrorlines ?plotting styles errorlines ?style yerrorlines ?with yerrorlines ?style errorlines ?with errorlines ?yerrorlines ?errorlines Ffigure_yerrorlines The `yerrorlines` (or `errorlines`) style is only relevant to 2D data plots. `yerrorlines` is like `linespoints`, except that a vertical error line is also drawn. At each point (x,y), a line is drawn from (x,y-ydelta) to (x,y+ydelta) or from (x,ylow) to (x,yhigh), depending on how many data columns are provided. The appearance of the tic mark at the ends of the bar is controlled by `set errorbars`. Either 3 or 4 input columns are required. 3 columns: x y ydelta 4 columns: x y ylow yhigh Additional input columns may be used to provide information such as variable point size, point type, or color. See also ^ <a href="https://www.apklas.com?arsae=http%3A%2F%2Fwww.gnuplot.info%2Fdemo%2Fmgr.html" target="_parent"> errorbar demo. ^ </a> #TeX \newpage 2 3D plots ?3D plots ?plotting styles 3D plots =3D 3D plots are generated using the command `splot` rather than `plot`. Many of the 2D plot styles (points, images, impulse, labels, vectors) can also be used in 3D by providing an extra column of data containing z coordinate. Some plot types (pm3d coloring, surfaces, contours) must be generated using the `splot` command even if only a 2D projection is wanted. 3 surface plots ?surface plots =surface Ffigure_surface+contours The styles `splot with lines` and `splot with surface` both generate a surface made from a grid of lines. Solid surfaces can be generated using the style `splot with pm3d`. Usually the surface is displayed at some convenient viewing angle, such that it clearly represents a 3D surface. See `set view`. In this case the X, Y, and Z axes are all visible in the plot. The illusion of 3D is enhanced by choosing hidden line removal. See `hidden3d`. The `splot` command can also calculate and draw contour lines corresponding to constant Z values. These contour lines may be drawn onto the surface itself, or projected onto the XY plane. See `set contour`. 3 2D projection (set view map) ?2D projection (set view map) Ffigure_mapcontours An important special case of the `splot` command is to map the Z coordinate onto a 2D surface by projecting the plot along the Z axis onto the xy plane. See `set view map`. This plot mode is useful for contour plots and heat maps. This figure shows contours plotted once with plot style `lines` and once with style `labels`. 3 PM3D plots ?PM3D PLOTS Ffigure_pm3dsolid 3D surfaces can also be drawn using solid pm3d quadrangles rather than lines. In this case there is no hidden surface removal, but if the component facets are drawn back-to-front then a similar effect is achieved. See `set pm3d depthorder`. While pm3d surfaces are by default colored using a smooth color palette (see `set palette`), it is also possible to specify a solid color surface or to specify distinct solid colors for the top and bottom surfaces as in the figure shown here. See `pm3d fillcolor`. Unlike the line-trimming in hidden3d mode, pm3d surfaces can be smoothly clipped to the current zrange. See `set pm3d clipping`. #TeX \newpage 2 Fence plots ?fenceplots =zerrorfill Ffigure_fenceplot Fence plots combine several 2D plots by aligning their Y coordinates and separating them from each other by a displacement along X. Filling the area between a base value and each plot's series of Z values enhances the visual impact of the alignment on Y and comparison on Z. There are several ways such plots can be created in gnuplot. The simplest is to use the 5 column variant of the `zerrorfill` style. Suppose there are separate curves z = Fi(y) indexed by i. A fence plot is generated by `splot with zerrorfill` using input columns i y z_base z_base Fi(y) 2 isosurface ?plotting styles isosurface ?style isosurface ?with isosurface ?isosurface Ffigure_isosurface This 3D plot style requires a populated voxel grid (see `set vgrid`, `vfill`). Linear interpolation of voxel grid values is used to estimate fractional grid coordinates corresponding to the requested isolevel. These points are then used to generate a tessellated surface. The facets making up the surface are rendered as pm3d polygons, so the surface coloring, transparency, and border properties are controlled by `set pm3d`. In general the surface is easier to interpret visually if facets are given a thin border that is darker than the fill color. By default the tessellation uses a mixture of quadrangles and triangles. To use triangle only, see `set isosurface`. Example: set style fill solid 0.3 set pm3d depthorder border lc "blue" lw 0.2 splot $helix with isosurface level 10 fc "cyan" 2 Zerrorfill ?plotting styles zerrorfill ?style zerrorfill ?with zerrorfill ?zerrorfill Syntax: splot DATA using 1:2:3:4[:5] with zerrorfill {fc|fillcolor <colorspec>} {lt|linetype <n>} {<line properties>} The `zerrorfill` plot style is similar to one variant of the 2D plot style `filledcurves`. It fills the area between two functions or data lines that are sampled at the same x and y points. It requires 4 or 5 input columns: 4 columns: x y z zdelta 5 columns: x y z zlow zhigh Ffigure_zerror The area between zlow and zhigh is filled and then a line is drawn through the z values. By default both the line and the fill area use the same color, but you can change this in the splot command. The fill area properties are also affected by the global fill style; see `set style fill`. If there are multiple curves in the splot command each new curve may occlude all previous curves. To get proper depth sorting so that curves can only be occluded by curves closer to the viewer, use `set pm3d depthorder base`. Unfortunately this causes all the filled areas to be drawn after all of the corresponding lines of z values. In order to see both the lines and the depth-sorted fill areas you probably will need to make the fill areas partially transparent or use pattern fill rather than solid fill. The fill area in the first two examples below is the same. splot 'data' using 1:2:3:4 with zerrorfill fillcolor "grey" lt black splot 'data' using 1:2:3:($3-$4):($3+$4) with zerrorfill splot '+' using 1:(const):(func1($1)):(func2($1)) with zerrorfill splot for [k=1:5] datafile[k] with zerrorfill lt black fc lt (k+1) This plot style can also be used to create fence plots. See `fenceplots`. 2 Animation ?animation Any of gnuplot's interactive terminals (qt win wxt x11 aqua) can be used to display an animation by plotting successive frames from the command line or from a script. Several non-mousing terminals also support some form of animation. See `term sixelgd`, `term kittycairo`. Two terminals can save an animation to a file for later playback locally or by embedding it a web page. See `term gif animate`, `term webp`. ^ <p align="center"> ^ <picture> ^ <source srcset="figure_spinning_d20.webp" type="image/webp"> ^ <img src="figure_static_d20.png"> ^ </source></picture> Example: unset border; unset tics; unset key; set view equal xyz set pm3d border linecolor "black" set term webp animate delay 50 set output 'spinning_d20.webp' do for [ang=1:360:2] { set view 60, ang splot 'icosahedron.dat' with polygons fc "gold" } unset output 1 Commands ?commands This section lists the commands acceptable to `gnuplot` in alphabetical order. Printed versions of this document contain all commands; the text available interactively may not be complete. Indeed, on some systems there may be no commands at all listed under this heading. Note that in most cases unambiguous abbreviations for command names and their options are permissible, i.e., "`p f(x) w li`" instead of "`plot f(x) with lines`". In the syntax descriptions, braces ({}) denote optional arguments and a vertical bar (|) separates mutually exclusive choices. 2 Break ?commands break ?break The `break` command is only meaningful inside the bracketed iteration clause of a `do` or `while` statement. It causes the remaining statements inside the bracketed clause to be skipped and iteration is terminated. Execution resumes at the statement following the closing bracket. See also `continue`. 2 cd ?commands cd ?cd The `cd` command changes the working directory. Syntax: cd '<directory-name>' The directory name must be enclosed in quotes. Examples: cd 'subdir' cd ".." It is recommended that Windows users use single-quotes, because backslash [\] has special significance inside double-quotes and has to be escaped. For example, cd "c:\newdata" fails, but cd 'c:\newdata' cd "c:\\newdata" work as expected. 2 call ?commands call ?call The `call` command is identical to the `load` command with one exception: the name of the file being loaded may be followed by up to nine parameters. call "inputfile" <param-1> <param-2> <param-3> ... <param-9> Gnuplot now provides a set of string variables ARG0, ARG1, ..., ARG9 and an integer variable ARGC. When a `call` command is executed ARG0 is set to the name of the input file, ARGC is set to the number of parameters present, and ARG1 to ARG9 are loaded from the parameters that follow it on the command line. Any existing contents of the ARG variables are saved and restored across a `call` command. Because the parameters ARG1 ... ARG9 are stored in ordinary string variables they may be dereferenced by macro expansion. However in many cases it is more natural to use them as you would any other variable. In parallel with the string representation of parameters ARG1 ... ARG9, the parameters themselves are stored in an array ARGV[9]. See `ARGV`. DEPRECATED: Versions prior to 5.0 performed macro-like substitution of the special tokens $0, $1, ... $9 with the literal contents of <param-1> ... That older mechanism is no longer supported. EXPERIMENTAL: Function blocks (new in this version) provide a more flexible alternative to `call`. See `function blocks`. 3 ARGV[ ] ?argv ?ARGV ?call argv ?call ARGV When a gnuplot script is entered via the `call` command any parameters passed by the caller are available via two mechanisms. Each parameter is stored as a string in variables ARG1, ARG2, ... ARG9. Each parameter is also stored as one element of the array ARGV[9]. Numerical values are stored as complex variables. All other values are stored as strings. ARGC holds the number of parameters. Thus after a call call 'routine_1.gp' 1 pi "title" The three arguments are available inside routine_1.gp as follows ARGC = 3 ARG1 = "1" ARGV[1] = 1.0 ARG2 = "3.14159" ARGV[2] = 3.14159265358979... ARG3 = "title" ARGV[3] = "title" In this example ARGV[1] and ARGV[2] have the full precision of a floating point variable. ARG2 lost precision in being stored as a string using format "%g". 3 Example ?call example ?commands call example Call site MYFILE = "script1.gp" FUNC = "sin(x)" call MYFILE FUNC 1.23 "This is a plot title" Upon entry to the called script ARG0 holds "script1.gp" ARG1 holds the string "sin(x)" ARG2 holds the string "1.23" ARG3 holds the string "This is a plot title" ARGC is 3 The script itself can now execute plot @ARG1 with lines title ARG3 print ARG2 * 4.56, @ARG2 * 4.56 print "This plot produced by script ", ARG0 Notice that because ARG1 is a string it must be dereferenced as a macro, but ARG2 may be dereferenced either as a macro (yielding a numerical constant) or a variable (yielding that same numerical value after auto-promotion of the string "1.23" to a real). The same result could be obtained directly from a shell script by invoking gnuplot with the `-c` command line option: gnuplot -persist -c "script1.gp" "sin(x)" 1.23 "This is a plot title" 2 clear ?commands clear ?clear =inset ?inset The `clear` command erases the current screen or output device as specified by `set terminal` and `set output`. This usually generates a formfeed on hardcopy devices. For some terminals `clear` erases only the portion of the plotting surface defined by `set size`, so for these it can be used in conjunction with `set multiplot` to create an inset. Example: set multiplot plot sin(x) set origin 0.5,0.5 set size 0.4,0.4 clear plot cos(x) unset multiplot Please see `set multiplot`, `set size`, and `set origin` for details. 2 Continue ?commands continue ?continue The `continue` command is only meaningful inside the bracketed iteration clause of a `do` or `while` statement. It causes the remaining statements inside the bracketed clause to be skipped. Execution resumes at the start of the next iteration (if any remain in the loop condition). See also `break`. 2 Do ?commands do ?do Syntax: do for <iteration-spec> { <commands> <commands> } Execute a sequence of commands multiple times. The commands must be enclosed in curly brackets, and the opening "{" must be on the same line as the `do` keyword. This command cannot be used with old-style (un-bracketed) if/else statements. See `if`. For examples of iteration specifiers, see `iteration`. Example: set multiplot layout 2,2 do for [name in "A B C D"] { filename = name . ".dat" set title sprintf("Condition %s",name) plot filename title name } unset multiplot See also `while`, `continue`, `break`. 2 evaluate ?commands evaluate ?evaluate The `evaluate` command executes gnuplot commands contained in a string or in a function block. Newline characters are not allowed within the string. evaluate "commands in a string constant" evaluate string_valued_function( ... arguments ... ) evaluate $functionblock( ... arguments ... ) This is especially useful for a repetition of similar commands. Example: set_label(x, y, text) \ = sprintf("set label '%s' at %f, %f point pt 5", text, x, y) eval set_label(1., 1., 'one/one') eval set_label(2., 1., 'two/one') eval set_label(1., 2., 'one/two') Please see `function blocks` and `substitution macros` for other mechanisms that construct or execute strings containing gnuplot commands. 2 exit ?commands exit ?exit exit exit message "error message text" exit status <integer error code> The commands `exit` and `quit`, as well as the END-OF-FILE character (usually Ctrl-D) terminate input from the current input stream: terminal session, pipe, or file input (pipe). If input streams are nested (inherited `load` scripts), then reading will continue in the parent stream. When the top level stream is closed, the program itself will exit. The command `exit gnuplot` will immediately and unconditionally cause gnuplot to exit even if the input stream is multiply nested. In this case any open output files may not be completed cleanly. Example of use: bind "ctrl-x" "unset output; exit gnuplot" The command `exit error "error message"` simulates a program error. In interactive mode it prints the error message and returns to the command line, breaking out of all nested loops or calls. In non-interactive mode the program will exit. When gnuplot exits to the controlling shell, the return value is not usually informative. This variant of the command allows you to return a specific value. exit status <value> See help for `batch/interactive` for more details. 2 fit ?commands fit ?fit ?least-squares ?Marquardt The `fit` command fits a user-supplied real-valued expression to a set of data points, using the nonlinear least-squares Marquardt-Levenberg algorithm. There can be up to 12 independent variables, there is always 1 dependent variable, and any number of parameters can be fitted. Optionally, error estimates can be input for weighting the data points. The basic use of `fit` is best explained by a simple example where a set of measured x and y values read from a file are used to be modeled by a function y = f(x). f(x) = a + b*x + c*x**2 fit f(x) 'measured.dat' using 1:2 via a,b,c plot 'measured.dat' u 1:2, f(x) Syntax: fit {<ranges>} <expression> '<datafile>' {datafile-modifiers} {{unitweights} | {y|xy|z}error | errors <var1>{,<var2>,...}} via '<parameter file>' | <var1>{,<var2>,...} Ranges may be specified to filter the data used in fitting. Out-of-range data points are ignored. The syntax is [{dummy_variable=}{<min>}{:<max>}], analogous to `plot`; see `plot ranges`. <expression> can be any valid `gnuplot` expression, although the most common is a previously user-defined function of the form f(x) or f(x,y). It must be real-valued. The names of the independent variables are set by the `set dummy` command, or in the <ranges> part of the command (see below); by default, the first two are called x and y. Furthermore, the expression should depend on one or more variables whose value is to be determined by the fitting procedure. <datafile> is treated as in the `plot` command. All the `plot datafile` modifiers (`using`, `every`,...) except `smooth` are applicable to `fit`. See `plot datafile`. The datafile contents can be interpreted flexibly by providing a `using` qualifier as with plot commands. For example to generate the independent variable x as the sum of columns 2 and 3, while taking z from column 6 and requesting equal weights: fit ... using ($2+$3):6 In the absence of a `using` specification, the fit implicitly assumes there is only a single independent variable. If the file itself, or the using specification, contains only a single column of data, the line number is taken as the independent variable. If a `using` specification is given, there can be up to 12 independent variables (and more if specially configured at compile time). The `unitweights` option, which is the default, causes all data points to be weighted equally. This can be changed by using the `errors` keyword to read error estimates of one or more of the variables from the data file. These error estimates are interpreted as the standard deviation s of the corresponding variable value and used to compute a weight for the datum as 1/s**2. In case of error estimates of the independent variables, these weights are further multiplied by fitting function derivatives according to the "effective variance method" (Jay Orear, Am. J. Phys., Vol. 50, 1982). The `errors` keyword is to be followed by a comma-separated list of one or more variable names for which errors are to be input; the dependent variable z must always be among them, while independent variables are optional. For each variable in this list, an additional column will be read from the file, containing that variable's error estimate. Again, flexible interpretation is possible by providing the `using` qualifier. Note that the number of independent variables is thus implicitly given by the total number of columns in the `using` qualifier, minus 1 (for the dependent variable), minus the number of variables in the `errors` qualifier. As an example, if one has 2 independent variables, and errors for the first independent variable and the dependent variable, one uses the `errors x,z` qualifier, and a `using` qualifier with 5 columns, which are interpreted as x:y:z:sx:sz (where x and y are the independent variables, z the dependent variable, and sx and sz the standard deviations of x and z). A few shorthands for the `errors` qualifier are available: `yerrors` (for fits with 1 column of independent variable), and `zerrors` (for the general case) are all equivalent to `errors z`, indicating that there is a single extra column with errors of the dependent variable. `xyerrors`, for the case of 1 independent variable, indicates that there are two extra columns, with errors of both the independent and the dependent variable. In this case the errors on x and y are treated by Orear's effective variance method. Note that `yerror` and `xyerror` are similar in both form and interpretation to the `yerrorlines` and `xyerrorlines` 2D plot styles. With the command `set fit v4` the fit command syntax is compatible with `gnuplot` version 4. In this case there must be two more `using` qualifiers (z and s) than there are independent variables, unless there is only one variable. `gnuplot` then uses the following formats, depending on the number of columns given in the `using` specification: z # 1 independent variable (line number) x:z # 1 independent variable (1st column) x:z:s # 1 independent variable (3 columns total) x:y:z:s # 2 independent variables (4 columns total) x1:x2:x3:z:s # 3 independent variables (5 columns total) x1:x2:x3:...:xN:z:s # N independent variables (N+2 columns total) Please beware that this means that you have to supply z-errors s in a fit with two or more independent variables. If you want unit weights you need to supply them explicitly by using e.g. then format x:y:z:(1). The dummy variable names may be changed when specifying a range as noted above. The first range corresponds to the first `using` spec, and so on. A range may also be given for z (the dependent variable), in which case data points for which f(x,...) is out of the z range will not contribute to the residual being minimized. Multiple datasets may be simultaneously fit with functions of one independent variable by making y a 'pseudo-variable', e.g., the dataline number, and fitting as two independent variables. See `fit multi-branch`. The `via` qualifier specifies which parameters are to be optimized, either directly, or by referencing a parameter file. Examples: f(x) = a*x**2 + b*x + c g(x,y) = a*x**2 + b*y**2 + c*x*y set fit limit 1e-6 fit f(x) 'measured.dat' via 'start.par' fit f(x) 'measured.dat' using 3:($7-5) via 'start.par' fit f(x) './data/trash.dat' using 1:2:3 yerror via a, b, c fit g(x,y) 'surface.dat' using 1:2:3 via a, b, c fit a0 + a1*x/(1 + a2*x/(1 + a3*x)) 'measured.dat' via a0,a1,a2,a3 fit a*x + b*y 'surface.dat' using 1:2:3 via a,b fit [*:*][yaks=*:*] a*x+b*yaks 'surface.dat' u 1:2:3 via a,b fit [][][t=*:*] a*x + b*y + c*t 'foo.dat' using 1:2:3:4 via a,b,c set dummy x1, x2, x3, x4, x5 h(x1,x2,x3,x4,s5) = a*x1 + b*x2 + c*x3 + d*x4 + e*x5 fit h(x1,x2,x3,x4,x5) 'foo.dat' using 1:2:3:4:5:6 via a,b,c,d,e After each iteration step, detailed information about the current state of the fit is written to the display. The same information about the initial and final states is written to a log file, "fit.log". This file is always appended to, so as to not lose any previous fit history; it should be deleted or renamed as desired. By using the command `set fit logfile`, the name of the log file can be changed. If activated by using `set fit errorvariables`, the error for each fitted parameter will be stored in a variable named like the parameter, but with "_err" appended. Thus the errors can be used as input for further computations. If `set fit prescale` is activated, fit parameters are prescaled by their initial values. This helps the Marquardt-Levenberg routine converge more quickly and reliably in cases where parameters differ in size by several orders of magnitude. The fit may be interrupted by pressing Ctrl-C (Ctrl-Break in wgnuplot). After the current iteration completes, you have the option to (1) stop the fit and accept the current parameter values, (2) continue the fit, (3) execute a `gnuplot` command as specified by `set fit script` or the environment variable `FIT_SCRIPT`. The default is `replot`, so if you had previously plotted both the data and the fitting function in one graph, you can display the current state of the fit. Once `fit` has finished, the `save fit` command may be used to store final values in a file for subsequent use as a parameter file. See `save fit` for details. 3 adjustable parameters ?commands fit parameters ?fit parameters ?commands fit adjustable_parameters ?fit adjustable_parameters ?fit_parameters There are two ways that `via` can specify the parameters to be adjusted, either directly on the command line or indirectly, by referencing a parameter file. The two use different means to set initial values. Adjustable parameters can be specified by a comma-separated list of variable names after the `via` keyword. Any variable that is not already defined is created with an initial value of 1.0. However, the fit is more likely to converge rapidly if the variables have been previously declared with more appropriate starting values. In a parameter file, each parameter to be varied and a corresponding initial value are specified, one per line, in the form varname = value Comments, marked by '#', and blank lines are permissible. The special form varname = value # FIXED means that the variable is treated as a 'fixed parameter', initialized by the parameter file, but not adjusted by `fit`. For clarity, it may be useful to designate variables as fixed parameters so that their values are reported by `fit`. The keyword `# FIXED` has to appear in exactly this form. 3 short introduction ?commands fit beginners_guide ?fit beginners_guide ?fit guide ?fitting `fit` is used to find a set of parameters that 'best' fits your data to your user-defined function. The fit is judged on the basis of the sum of the squared differences or 'residuals' (SSR) between the input data points and the function values, evaluated at the same places. This quantity is often called 'chisquare' (i.e., the Greek letter chi, to the power of 2). The algorithm attempts to minimize SSR, or more precisely the weighted sum of squared residuals (WSSR), for which the residuals are weighted by the input data errors before being squared; see `fit error_estimates` for details. That's why it is called 'least-squares fitting'. Let's look at an example to see what is meant by 'non-linear', but first we had better go over some terms. Here it is convenient to use z as the dependent variable for user-defined functions of either one independent variable, z=f(x), or two independent variables, z=f(x,y). A parameter is a user-defined variable that `fit` will adjust, i.e., an unknown quantity in the function declaration. Linearity/non-linearity refers to the relationship of the dependent variable, z, to the parameters which `fit` is adjusting, not of z to the independent variables, x and/or y. (To be technical, the second {and higher} derivatives of the fitting function with respect to the parameters are zero for a linear least-squares problem). For linear least-squares the user-defined function will be a sum of simple functions, not involving any parameters, each multiplied by one parameter. Nonlinear least-squares handles more complicated functions in which parameters can be used in a large number of ways. An example that illustrates the difference between linear and nonlinear least-squares is the Fourier series. One member may be written as z=a*sin(c*x) + b*cos(c*x). If a and b are the unknown parameters and c is constant, then estimating values of the parameters is a linear least-squares problem. However, if c is an unknown parameter, the problem is nonlinear. In the linear case, parameter values can be determined by comparatively simple linear algebra, in one direct step. However the linear special case is also solved along with more general nonlinear problems by the iterative procedure that `gnuplot` uses. `fit` attempts to find the minimum by doing a search. Each step (iteration) calculates WSSR with a new set of parameter values. The Marquardt-Levenberg algorithm selects the parameter values for the next iteration. The process continues until a preset criterion is met, either (1) the fit has "converged" (the relative change in WSSR is less than a certain limit, see `set fit limit`), or (2) it reaches a preset iteration count limit (see `set fit maxiter`). The fit may also be interrupted and subsequently halted from the keyboard (see `fit`). The user variable FIT_CONVERGED contains 1 if the previous fit command terminated due to convergence; it contains 0 if the previous fit terminated for any other reason. FIT_NITER contains the number of iterations that were done during the last fit. Often the function to be fitted will be based on a model (or theory) that attempts to describe or predict the behaviour of the data. Then `fit` can be used to find values for the free parameters of the model, to determine how well the data fits the model, and to estimate an error range for each parameter. See `fit error_estimates`. Alternatively, in curve-fitting, functions are selected independent of a model (on the basis of experience as to which are likely to describe the trend of the data with the desired resolution and a minimum number of parameters*functions.) The `fit` solution then provides an analytic representation of the curve. However, if all you really want is a smooth curve through your data points, the `smooth` option to `plot` may be what you've been looking for rather than `fit`. 3 error estimates ?commands fit error_estimates ?fit error_estimates ?fit errors In `fit`, the term "error" is used in two different contexts, data error estimates and parameter error estimates. Data error estimates are used to calculate the relative weight of each data point when determining the weighted sum of squared residuals, WSSR or chisquare. They can affect the parameter estimates, since they determine how much influence the deviation of each data point from the fitted function has on the final values. Some of the `fit` output information, including the parameter error estimates, is more meaningful if accurate data error estimates have been provided. The `statistical overview` describes some of the `fit` output and gives some background for the 'practical guidelines'. 4 statistical overview ?commands fit error statistical_overview ?statistical_overview The theory of non-linear least-squares is generally described in terms of a normal distribution of errors, that is, the input data is assumed to be a sample from a population having a given mean and a Gaussian (normal) distribution about the mean with a given standard deviation. For a sample of sufficiently large size, and knowing the population standard deviation, one can use the statistics of the chisquare distribution to describe a "goodness of fit" by looking at the variable often called "chisquare". Here, it is sufficient to say that a reduced chisquare (chisquare/degrees of freedom, where degrees of freedom is the number of datapoints less the number of parameters being fitted) of 1.0 is an indication that the weighted sum of squared deviations between the fitted function and the data points is the same as that expected for a random sample from a population characterized by the function with the current value of the parameters and the given standard deviations. If the standard deviation for the population is not constant, as in counting statistics where variance = counts, then each point should be individually weighted when comparing the observed sum of deviations and the expected sum of deviations. At the conclusion `fit` reports 'stdfit', the standard deviation of the fit, which is the rms of the residuals, and the variance of the residuals, also called 'reduced chisquare' when the data points are weighted. The number of degrees of freedom (the number of data points minus the number of fitted parameters) is used in these estimates because the parameters used in calculating the residuals of the datapoints were obtained from the same data. If the data points have weights, `gnuplot` calculates the so-called p-value, i.e. one minus the cumulative distribution function of the chisquare-distribution for the number of degrees of freedom and the resulting chisquare, see `fit practical_guidelines`. These values are exported to the variables FIT_NDF = Number of degrees of freedom FIT_WSSR = Weighted sum-of-squares residual FIT_STDFIT = sqrt(WSSR/NDF) FIT_P = p-value To estimate confidence levels for the parameters, one can use the minimum chisquare obtained from the fit and chisquare statistics to determine the value of chisquare corresponding to the desired confidence level, but considerably more calculation is required to determine the combinations of parameters which produce such values. Rather than determine confidence intervals, `fit` reports parameter error estimates which are readily obtained from the variance-covariance matrix after the final iteration. By convention, these estimates are called "standard errors" or "asymptotic standard errors", since they are calculated in the same way as the standard errors (standard deviation of each parameter) of a linear least-squares problem, even though the statistical conditions for designating the quantity calculated to be a standard deviation are not generally valid for a nonlinear least-squares problem. The asymptotic standard errors are generally over-optimistic and should not be used for determining confidence levels, but are useful for qualitative purposes. The final solution also produces a correlation matrix indicating correlation of parameters in the region of the solution; The main diagonal elements, autocorrelation, are always 1; if all parameters were independent, the off-diagonal elements would be nearly 0. Two variables which completely compensate each other would have an off-diagonal element of unit magnitude, with a sign depending on whether the relation is proportional or inversely proportional. The smaller the magnitudes of the off-diagonal elements, the closer the estimates of the standard deviation of each parameter would be to the asymptotic standard error. 4 practical guidelines ?commands fit error practical_guidelines ?fit practical_guidelines ?fit guidelines If you have a basis for assigning weights to each data point, doing so lets you make use of additional knowledge about your measurements, e.g., take into account that some points may be more reliable than others. That may affect the final values of the parameters. Weighting the data provides a basis for interpreting the additional `fit` output after the last iteration. Even if you weight each point equally, estimating an average standard deviation rather than using a weight of 1 makes WSSR a dimensionless variable, as chisquare is by definition. Each fit iteration will display information which can be used to evaluate the progress of the fit. (An '*' indicates that it did not find a smaller WSSR and is trying again.) The 'sum of squares of residuals', also called 'chisquare', is the WSSR between the data and your fitted function; `fit` has minimized that. At this stage, with weighted data, chisquare is expected to approach the number of degrees of freedom (data points minus parameters). The WSSR can be used to calculate the reduced chisquare (WSSR/ndf) or stdfit, the standard deviation of the fit, sqrt(WSSR/ndf). Both of these are reported for the final WSSR. If the data are unweighted, stdfit is the rms value of the deviation of the data from the fitted function, in user units. If you supplied valid data errors, the number of data points is large enough, and the model is correct, the reduced chisquare should be about unity. (For details, look up the 'chi-squared distribution' in your favorite statistics reference.) If so, there are additional tests, beyond the scope of this overview, for determining how well the model fits the data. A reduced chisquare much larger than 1.0 may be due to incorrect data error estimates, data errors not normally distributed, systematic measurement errors, 'outliers', or an incorrect model function. A plot of the residuals, e.g., `plot 'datafile' using 1:($2-f($1))`, may help to show any systematic trends. Plotting both the data points and the function may help to suggest another model. Similarly, a reduced chisquare less than 1.0 indicates WSSR is less than that expected for a random sample from the function with normally distributed errors. The data error estimates may be too large, the statistical assumptions may not be justified, or the model function may be too general, fitting fluctuations in a particular sample in addition to the underlying trends. In the latter case, a simpler function may be more appropriate. The p-value of the fit is one minus the cumulative distribution function of the chisquare-distribution for the number of degrees of freedom and the resulting chisquare. This can serve as a measure of the goodness-of-fit. The range of the p-value is between zero and one. A very small or large p-value indicates that the model does not describe the data and its errors well. As described above, this might indicate a problem with the data, its errors or the model, or a combination thereof. A small p-value might indicate that the errors have been underestimated and the errors of the final parameters should thus be scaled. See also `set fit errorscaling`. You'll have to get used to both `fit` and the kind of problems you apply it to before you can relate the standard errors to some more practical estimates of parameter uncertainties or evaluate the significance of the correlation matrix. Note that `fit`, in common with most nonlinear least-squares implementations, minimizes the weighted sum of squared distances (y-f(x))**2. It does not provide any means to account for "errors" in the values of x, only in y. Also, any "outliers" (data points outside the normal distribution of the model) will have an exaggerated effect on the solution. 3 control ?commands fit control ?fit control =FIT_LOG =FIT_SCRIPT There are two environment variables that can be defined to affect `fit`. The environment variables must be defined before `gnuplot` is executed; how to do so depends on your operating system. FIT_LOG changes the name (and/or path) of the file to which the fit log will be written. The default is to write "fit.log" in the current working directory. This can be overwritten at run time using the command `set fit logfile`. FIT_SCRIPT specifies a command that may be executed after an user interrupt. The default is `replot`, but a `plot` or `load` command may be useful to display a plot customized to highlight the progress of the fit. This can be changed at run time using `set fit script`. For many other run time adjustments to way fit works, see `set fit`. 3 error recovery ?commands fit error_recovery ?fit error_recovery Starting with gnuplot version 6, the `fit` command always returns to the next command input line regardless of the success or failure of fitting. This allows scripted recovery from fit errors. The variable FIT_ERROR is set to 0 on success, non-zero on error. This example plots however many of five data sets can be successfully fit. Failure for data set 2 would not prevent fitting data sets 3 through 5. do for [i=1:5] { DATA = sprintf("Data_%05d.dat", i) fit f(x) DATA via a,b,c if (FIT_ERROR || !FIT_CONVERGED) { print "Fit failed for ", DATA continue } set output sprintf("dataset_%05.png", i) plot DATA, f(x) unset output } 3 multi-branch ?commands fit multi-branch ?fit multi-branch ?multi-branch ?branch In multi-branch fitting, multiple data sets can be simultaneously fit with functions of one independent variable having common parameters by minimizing the total WSSR. The function and parameters (branch) for each data set are selected by using a 'pseudo-variable', e.g., either the dataline number (a 'column' index of -1) or the datafile index (-2), as the second independent variable. Example: Given two exponential decays of the form, z=f(x), each describing a different data set but having a common decay time, estimate the values of the parameters. If the datafile has the format x:z:s, then f(x,y) = (y==0) ? a*exp(-x/tau) : b*exp(-x/tau) fit f(x,y) 'datafile' using 1:-2:2:3 via a, b, tau For a more complicated example, see the file "hexa.fnc" used by the "fit.dem" demo. Appropriate weighting may be required since unit weights may cause one branch to predominate if there is a difference in the scale of the dependent variable. Fitting each branch separately, using the multi-branch solution as initial values, may give an indication as to the relative effect of each branch on the joint solution. 3 starting values ?commands fit starting_values ?fit starting_values ?starting_values Nonlinear fitting is not guaranteed to converge to the global optimum (the solution with the smallest sum of squared residuals, SSR), and can get stuck at a local minimum. The routine has no way to determine that; it is up to you to judge whether this has happened. `fit` may, and often will get "lost" if started far from a solution, where SSR is large and changing slowly as the parameters are varied, or it may reach a numerically unstable region (e.g., too large a number causing a floating point overflow) which results in an "undefined value" message or `gnuplot` halting. To improve the chances of finding the global optimum, you should set the starting values at least roughly in the vicinity of the solution, e.g., within an order of magnitude, if possible. The closer your starting values are to the solution, the less chance of stopping at a false minimum. One way to find starting values is to plot data and the fitting function on the same graph and change parameter values and `replot` until reasonable similarity is reached. The same plot is also useful to check whether the fit found a false minimum. Of course finding a nice-looking fit does not prove there is no "better" fit (in either a statistical sense, characterized by an improved goodness-of-fit criterion, or a physical sense, with a solution more consistent with the model.) Depending on the problem, it may be desirable to `fit` with various sets of starting values, covering a reasonable range for each parameter. 3 time data ?commands fit time_data ?fit time_data In fitting time data it is important to remember that gnuplot represents time as seconds since 1 January 1970. For example if you wanted to fit a quadratic model for the time dependence of something measured over the course of one day in 2023, you might expect that it could be done using T(x) = a + b*x + c*x*x set xdata time fit T(x) 'hits.dat' using 1:3 via a,b,c This will probably fail, because internally the x values corresponding to that one day will have a range something like [1.67746e+09 : 1.67754e+09]. The fractional change in x across the measured data will be only about 1.e-05 and to guarantee convergence you would probably need many decimal places of accuracy in the initial parameter estimates. One solution is to recast the problem as change in time since the start of measurement. set xdata time # data format "27-02-2023 12:00:00 measurement" timefmt = "%d-%m-%Y %H:%M:%S" set timefmt timefmt t0 = strptime( timefmt, "27-02-2023 00:00:00" ) fit T(x) 'temperature.dat' using ($1-t0):3 via a,b,c This shifts the range of the data to [0 : 86400], which is more tractable. Another possibility in this case is to ignore the date in column 1 and use relative time formats (tH/tM/tS) applied to column 2. set timefmt "%tH:%tM:%tS" fit T(x) 'temperature.dat' using 2:3 via a,b,c 3 tips ?commands fit tips ?fit tips ?tips Here are some tips to keep in mind to get the most out of `fit`. They're not very organized, so you'll have to read them several times until their essence has sunk in. The two forms of the `via` argument to `fit` serve two largely distinct purposes. The `via "file"` form is best used for (possibly unattended) batch operation, where you supply the starting parameter values in a file. The `via var1, var2, ...` form is best used interactively, where the command history mechanism may be used to edit the list of parameters to be fitted or to supply new startup values for the next try. This is particularly useful for hard problems, where a direct fit to all parameters at once won't work without good starting values. To find such, you can iterate several times, fitting only some of the parameters, until the values are close enough to the goal that the final fit to all parameters at once will work. Make sure that there is no mutual dependency among parameters of the function you are fitting. For example, don't try to fit a*exp(x+b), because a*exp(x+b)=a*exp(b)*exp(x). Instead, fit either a*exp(x) or exp(x+b). A technical issue: The larger the ratio of the largest and the smallest absolute parameter values, the slower the fit will converge. If the ratio is close to or above the inverse of the machine floating point precision, it may take next to forever to converge, or refuse to converge at all. You will either have to adapt your function to avoid this, e.g., replace 'parameter' by '1e9*parameter' in the function definition, and divide the starting value by 1e9 or use `set fit prescale` which does this internally according to the parameter starting values. If you can write your function as a linear combination of simple functions weighted by the parameters to be fitted, by all means do so. That helps a lot, because the problem is no longer nonlinear and should converge with only a small number of iterations, perhaps just one. Some prescriptions for analysing data, given in practical experimentation courses, may have you first fit some functions to your data, perhaps in a multi-step process of accounting for several aspects of the underlying theory one by one, and then extract the information you really wanted from the fitting parameters of those functions. With `fit`, this may often be done in one step by writing the model function directly in terms of the desired parameters. Transforming data can also quite often be avoided, though sometimes at the cost of a more difficult fit problem. If you think this contradicts the previous paragraph about simplifying the fit function, you are correct. A "singular matrix" message indicates that this implementation of the Marquardt-Levenberg algorithm can't calculate parameter values for the next iteration. Try different starting values, writing the function in another form, or a simpler function. Finally, a nice quote from the manual of another fitting package (fudgit), that kind of summarizes all these issues: "Nonlinear fitting is an art!" #TeX \newpage 2 function blocks ?commands function ?function blocks ?functionblocks The `function` command signals the definition of a here-document containing a named block of gnuplot code that can be called as a function. As with data blocks, the name of a function block must begin with a '$'. Up to nine named parameters may be specified as part of the definition. These names may be used inside the function block as local variables. See `local` and `scope`. Once the function block is defined, you can invoke it by name anywhere that a normal function could be used. If the return value is not relevant, the function block may be invoked by an "evaluate" command rather than as part of an assignment expression. Example: function $sinc(arg) << EOF if (arg == 0) { return 1.0 } return sin(arg) / arg EOF gnuplot> plot $sinc(x) with lines title "sinc(x) as a function block" It is not necessary to specify a list of named arguments to a function block at the time it is declared. Arguments to the function passed from the command line can be also be accessed from inside the function block as ARGV[1] etc, as they would be for a `call` command. See `ARGV`. This allows defining a function block that can operate on a variable number of arguments. Example: function $max << EOF local max = real("-Inf") if (ARGC == 0) { return NaN } do for [i=1:ARGC] { if (max < ARGV[i]) { max = ARGV[i] } } return max EOF gnuplot> foo = $max( f(A), 2.0, C, Array[3] ) gnuplot> baz = $max( foo, 100. ) The primary motivation for function block support is to allow definition of complicated functions directly in gnuplot. Execution is of course slower than if the same function were coded in C or Fortran, but this is acceptable for many purposes. If execution speed matters then the function can be implemented later as a plugin instead (see `plugins`). A second use for function blocks is to allow execution of gnuplot commands in a context they otherwise could not appear. Suppose for example you want to plot data from two csv files, but one file uses comma-separated fields while the other uses semicolon-separated fields. Normally this property would have been set by a previous `set datafile` command and would have to match all files used by the plot command. However we can define a function block to invoke as a definition immediately before each file is referenced in the plot. function $set_csv(char) << EOF set datafile separator char EOF plot tmp=$set_csv(",") FILE1, tmp=$set_csv(";") FILE2 Limitations: #start #b Data blocks and function blocks cannot be defined inside a function block. #b These commands cannot be executed inside a function block: ## `reset`, `shell`, `!<shell command>`. #b A `plot`, `replot`, `splot`, `refresh`, `stats`, `vfill`, or `fit` command ## is accepted in a function block only if none of those commands is already ## in progress. E.g. you cannot use `stats` in a function block called by a ## `plot` command, you cannot invoke `plot` from inside a `fit` command, etc. #end A non-trivial example of using function blocks to implement and plot a 15-term Lanczos approximation for the complex lngamma function is provided in the demo collection as ^ <a href="https://www.apklas.com?arsae=http%3A%2F%2Fwww.gnuplot.info%2Fdemo_6.0%2Ffunction_block.html" target="_parent"> function_block.dem ^ </a> The function block implementation is slower by a factor of roughly 25 compared to the built-in lnGamma function using the same algorithm coded directly in C. Nevertheless it is still fast enough for 3D interactive rotation. #TeX The function definitions used in that demo are show below. #TeX \newline #TeX \begin{center} #TeX \begin{minipage}{5in} #TeX { #TeX Function block implementation of $log\Gamma(z)$ using a 15-term Lanczos approximation #TeX \hrule #TeX ~\newline #TeX \small #TeX \begin{verbatim} #TeX array coef[15] = [ ... ] #TeX #TeX function $Lanczos(z) << EOD #TeX local Sum = coef[1] + sum [k=2:15] coef[k] / (z + k - 1) #TeX local temp = z + 671./128. #TeX temp = (z + 0.5) * log(temp) - temp #TeX temp = temp + log( sqrt(2*pi) * Sum/z ) #TeX return temp #TeX EOD #TeX #TeX function $Reflect(z) << EOD #TeX local w = $Lanczos(1.0 - z) #TeX local temp = log( sin(pi * z) ) #TeX return log(pi) - (w + temp) #TeX EOD #TeX #TeX my_lngamma(z) = (z == 0) ? NaN : (real(z) < 0.5) ? $Reflect(z) : $Lanczos(z) #TeX \end{verbatim} #TeX \hrule #TeX } #TeX \end{minipage} #TeX \end{center} Use of function blocks is EXPERIMENTAL. Details may change before inclusion in a release version. #TeX \newpage 2 help ?commands help ?help The `help` command displays built-in help. To specify information on a particular topic use the syntax: help {<topic>} If <topic> is not specified, a short message is printed about `gnuplot`. After help for the requested topic is given, a menu of subtopics is given; help for a subtopic may be requested by typing its name, extending the help request. After that subtopic has been printed, the request may be extended again or you may go back one level to the previous topic. Eventually, the `gnuplot` command line will return. If a question mark (?) is given as the topic, the list of topics currently available is printed on the screen. 2 history ?commands history ?history The `history` command prints or saves previous commands in the history list, or reexecutes a previous entry in the list. To modify the behavior of this command or the location of the saved history file, see `set history`. Input lines with `history` as their first command are not stored in the command history. Examples: history # show the complete history history 5 # show last 5 entries in the history history quiet 5 # show last 5 entries without entry numbers history "hist.gp" # write the complete history to file hist.gp history "hist.gp" append # append the complete history to file hist.gp history 10 "hist.gp" # write last 10 commands to file hist.gp history 10 "|head -5 >>diary.gp" # write 5 history commands using pipe history ?load # show all history entries starting with "load" history ?"set c" # like above, several words enclosed in quotes hist !"set xr" # like above, several words enclosed in quotes hist !55 # reexecute the command at history entry 55 2 if ?commands if ?if Syntax: if (<condition>) { <commands>; <commands> <commands> } else if (<condition>) { <commands> } else { <commands> } This version of gnuplot supports block-structured if/else statements. If the keyword `if` or `else` is immediately followed by an opening "{", then conditional execution applies to all statements, possibly on multiple input lines, until a matching "}" terminates the block. If commands may be nested. Prior to gnuplot version 5 the scope of if/else commands was limited to a single input line. Now a multi-line clause may be enclosed in curly brackets. The old syntax is still honored but cannot be used inside a bracketed clause. Old syntax: if (<condition>) <command-line> [; else if (<condition>) ...; else ...] If no opening "{" follows the `if` keyword, the command(s) in <command-line> will be executed if <condition> is true (non-zero) or skipped if <condition> is false (zero). Either case will consume commands on the input line until the end of the line or an occurrence of `else`. Note that use of `;` to allow multiple commands on the same line will _not_ end the conditionalized commands. 2 for ?for The `plot`, `splot`, `set` and `unset` commands may optionally contain an iteration clause. This has the effect of executing the basic command multiple times, each time re-evaluating any expressions that make use of the iteration control variable. Iteration of arbitrary command sequences can be requested using the `do` command. Two forms of iteration clause are currently supported: for [intvar = start:end{:increment}] for [stringvar in "A B C D"] Examples: plot for [filename in "A.dat B.dat C.dat"] filename using 1:2 with lines plot for [basename in "A B C"] basename.".dat" using 1:2 with lines set for [i = 1:10] style line i lc rgb "blue" unset for [tag = 100:200] label tag Nested iteration is supported: set for [i=1:9] for [j=1:9] label i*10+j sprintf("%d",i*10+j) at i,j See additional documentation for `iteration`, `do`. 2 import ?commands import ?import =plugins The `import` command associates a user-defined function name with a function exported by an external shared object. This constitutes a plugin mechanism that extends the set of functions available in gnuplot. Syntax: import func(x[,y,z,...]) from "sharedobj[:symbol]" Examples: # make the function myfun, exported by "mylib.so" or "mylib.dll" # available for plotting or numerical calculation in gnuplot import myfun(x) from "mylib" import myfun(x) from "mylib:myfun" # same as above # make the function theirfun, defined in "theirlib.so" or "theirlib.dll" # available under a different name import myfun(x,y,z) from "theirlib:theirfun" The program extends the name given for the shared object by either ".so" or ".dll" depending on the operating system, and searches for it first as a full path name and then as a path relative to the current directory. The operating system itself may also search any directories in LD_LIBRARY_PATH or DYLD_LIBRARY_PATH. See `plugins`. 2 load ?commands load ?load The `load` command executes each line of the specified input file as if it had been typed in interactively. Files created by the `save` command can later be `load`ed. Any text file containing valid gnuplot commands can be executed by a `load` command. Files being loaded may themselves contain `load` or `call` commands. To pass arguments to a loaded file, see `call`. Syntax: load "<input-file>" load $datablock The name of the input file must be enclosed in quotes. The special filename "-" may be used to `load` commands from standard input. This allows a `gnuplot` command file to accept some commands from standard input. Please see help for `batch/interactive` for more details. On systems that support a popen function, the load file can be read from a pipe by starting the file name with a '<'. Examples: load 'work.gnu' load "func.dat" load "< loadfile_generator.sh" The `load` command is performed implicitly on any file names given as arguments to `gnuplot`. These are loaded in the order specified, and then `gnuplot` exits. EXPERIMENTAL: It is also possible to execute commands from lines of text stored internally. See `function blocks`. A function block may be defined in-line or in an external file. Once the function block has been defined the commands may be executed repeatedly using `evaluate` on the internal copy rather than reloading the file. 2 local ?local ?commands local Syntax: local foo = <expression> local array foo[size] The `local` keyword introduces declaration of a variable whose scope is limited to the execution of the code block in which it is declared. Declaration is optional, but without it all variables are global. If the name of a local variable duplicates the name of a global variable, the global variable is shadowed until exit from the local scope. See `scope`. Local declarations may be used to prevent a global variable from being unintentionally overwritten by a `call` or `load` statement. They are particularly useful inside a function block. The `local` command is also valid inside the code block in curly brackets following an `if`, `else`, `do for`, or `while` statement. Example: Suppose you want to write a script "plot_all_data.gp" containing commands that plot a bunch of data sets. You want to call this convenience script from the command line or from other scripts without worrying that it trashes any variables with names "file" or "files" or "dataset" or "outfile". The variable "file" is inherently local because it is an iteration variable (see `scope`) but the other three names need keyword `local` to protect them. plot_all_data.gp: local files = system("ls -1 *.dat") do for [file in files] { local dataset = file[1:strstrt(file,".dat")-1] local outfile = dataset . ".png" set output outfile plot file with lines title dataset } unset output 2 lower See `raise`. 2 pause ?commands pause ?pause ?pause mouse The `pause` command displays any text associated with the command and then waits a specified amount of time or until the carriage return is pressed. `pause` is especially useful in conjunction with `load` files. Syntax: pause <time> {"<string>"} pause mouse {<endcondition>}{, <endcondition>} {"<string>"} pause mouse close <time> may be any constant or floating-point expression. `pause -1` will wait until a carriage return is hit, zero (0) won't pause at all, and a positive number will wait the specified number of seconds. If the current terminal supports `mousing`, then `pause mouse` will terminate on either a mouse click or on ctrl-C. For all other terminals, or if mousing is not active, `pause mouse` is equivalent to `pause -1`. If one or more end conditions are given after `pause mouse`, then any one of the conditions will terminate the pause. The possible end conditions are `keypress`, `button1`, `button2`, `button3`, `close`, and `any`. If the pause terminates on a keypress, then the ascii value of the key pressed is returned in MOUSE_KEY. The character itself is returned as a one character string in MOUSE_CHAR. Hotkeys (bind command) are disabled if keypress is one of the end conditions. Zooming is disabled if button3 is one of the end conditions. In all cases the coordinates of the mouse are returned in variables MOUSE_X, MOUSE_Y, MOUSE_X2, MOUSE_Y2. See `mouse variables`. Note: Since `pause` communicates with the operating system rather than the graphics, it may behave differently with different device drivers (depending upon how text and graphics are mixed). Examples: pause -1 # Wait until a carriage return is hit pause 3 # Wait three seconds pause -1 "Hit return to continue" pause 10 "Isn't this pretty? It's a cubic spline." pause mouse "Click any mouse button on selected data point" pause mouse keypress "Type a letter from A-F in the active window" pause mouse button1,keypress pause mouse any "Any key or button will terminate" The variant "pause mouse key" will resume after any keypress in the active plot window. If you want to wait for a particular key to be pressed, you can use a loop such as: print "I will resume after you hit the Tab key in the plot window" plot <something> pause mouse key while (MOUSE_KEY != 9) { pause mouse key } 3 pause mouse close ?commands pause mouse close ?pause mouse close ?pause close The command `pause mouse close` is a specific example of pausing to wait for an external event. In this case the program waits for a "close" event from the plot window. Exactly how to generate such an event varies with your desktop environment and configuration, but usually you can close the plot window by clicking on some widget on the window border or by typing a hot-key sequence such as <alt><f4> or <ctrl>q. If you are unsure whether a suitable widget or hot-key is available to the user, you may also want to define a hot-key sequence using gnuplot's own mechanism. See `bind`. The command sequence below may be useful when running gnuplot from a script rather than from the command line. plot <...whatever...> bind all "alt-End" "exit gnuplot" pause mouse close 3 pseudo-mousing during pause ?commands pause pseudo-mousing ?pseudo-mousing Some terminals use the same window for text entry and graphical display, including terminal types `dumb`, `sixel`, `kitty`, and `domterm`. These terminals do not currently support mousing per se, but during a `pause mouse` command they interpret keystrokes in the same way that a mousing terminal would. I.e. `l` toggles log-scale axes, `a` autoscales the current plot, left/right/up/down arrow keys change the view angle of 3D plots and perform incremental pan/zoom steps for 2D plots. `h` displays a list of key bindings. A carriage return terminates the `pause` and restores normal command line processing. 2 plot ?commands plot ?plot `plot` and `splot` are the primary commands for drawing plots with `gnuplot`. They offer many different graphical representations for functions and data. `plot` is used to draw 2D functions and data. `splot` draws 2D projections of 3D surfaces and data. Syntax: plot {<ranges>} <plot-element> {, <plot-element>, <plot-element>} Each plot element consists of a definition, a function, or a data source together with optional properties or modifiers: plot-element: {<iteration>} <definition> | {sampling-range} <function> | <data source> | keyentry {axes <axes>} {<title-spec>} {with <style>} The graphical representation of each plot element is determined by the keyword `with`, e.g. `with lines` or `with boxplot`. See `plotting styles`. The data to be plotted is either generated by a function (two functions if in parametric mode), read from a data file, read from a named data block that was defined previously, or extracted from an array. Multiple datafiles, data blocks, arrays, and/or functions may be plotted in a single plot command separated by commas. See `data`, `inline data`, `functions`. A plot-element that contains the definition of a function or variable does not create any visible output, see third example below. Examples: plot sin(x) plot sin(x), cos(x) plot f(x) = sin(x*a), a = .2, f(x), a = .4, f(x) plot "datafile.1" with lines, "datafile.2" with points plot [t=1:10] [-pi:pi*2] tan(t), \ "data.1" using (tan($2)):($3/$4) smooth csplines \ axes x1y2 notitle with lines 5 plot for [datafile in "spinach.dat broccoli.dat"] datafile See also `show plot`. 3 axes ?commands plot axes ?plot axes ?axes There are four possible sets of axes available; the keyword <axes> is used to select the axes for which a particular line should be scaled. `x1y1` refers to the axes on the bottom and left; `x2y2` to those on the top and right; `x1y2` to those on the bottom and right; and `x2y1` to those on the top and left. Ranges specified on the `plot` command apply only to the first set of axes (bottom left). 3 binary ?binary ?data binary ?datafile binary ?plot data binary BINARY DATA FILES: It is necessary to provide the keyword `binary` after the filename. Adequate details of the file format must be given on the command line or extracted from the file itself for a supported binary `filetype`. In particular, there are two structures for binary files, binary matrix format and binary general format. The `binary matrix` format contains a two dimensional array of 32 bit IEEE float values plus an additional column and row of coordinate values. In the `using` specifier of a plot command, column 1 refers to the matrix row coordinate, column 2 refers to the matrix column coordinate, and column 3 refers to the value stored in the array at those coordinates. The `binary general` format contains an arbitrary number of columns for which information must be specified at the command line. For example, `array`, `record`, `format` and `using` can indicate the size, format and dimension of data. There are a variety of useful commands for skipping file headers and changing endianess. There are a set of commands for positioning and translating data since often coordinates are not part of the file when uniform sampling is inherent in the data. Unlike reading from a text or matrix binary file, general binary does not treat the generated columns as 1, 2 or 3 in the `using` list. Instead column 1 refers to column 1 of the file, or as specified in the `format` list. There are global default settings for the various binary options which may be set using the same syntax as the options when used as part of the `(s)plot <filename> binary ...` command. This syntax is `set datafile binary ...`. The general rule is that common command-line specified parameters override file-extracted parameters which override default parameters. `Binary matrix` is the default binary format when no keywords specific to `binary general` are given, i.e., `array`, `record`, `format`, `filetype`. General binary data can be entered at the command line via the special file name '-'. However, this is intended for use through a pipe where programs can exchange binary data, not for keyboards. There is no "end of record" character for binary data. Gnuplot continues reading from a pipe until it has read the number of points declared in the `array` qualifier. See `binary matrix` or `binary general` for more details. The `index` keyword is not supported, since the file format allows only one surface per file. The `every` and `using` specifiers are supported. `using` operates as if the data were read in the above triplet form. ^ <a href="http://www.gnuplot.info/demo/binary.html"> Binary File Splot Demo. ^ </style></title-spec></axes></data></function></definition></iteration></plot-element></plot-element></plot-element></ranges></ctrl></f4></alt></something></time></string></endcondition></endcondition></string></time></expression></input-file></condition></condition></command-line></condition></command-line></condition></commands></commands></condition></commands></commands></commands></condition></topic></topic></shell></datafile></ranges></expression></max></min></var2></var1></parameter></var2></var1></datafile></expression></ranges></value></integer></commands></commands></iteration-spec></param-1></param-9></param-3></param-2></param-1></directory-name></p></line></n></colorspec></colorspec></fillstyle></y></x></radius></line></xpos></p></y-offset></baseline></data></x-coord></x-coord></x-coord></fillstyle></linetype></colorspec> 4 general ?commands plot binary general ?commands splot binary general ?plot binary general ?splot binary general ?datafile binary general ?data binary general ?binary general The `binary` keyword appearing alone indicates a binary data file that contains both coordinate information describing a non-uniform grid and the value of each grid point (see `binary matrix`). Binary data in any other format requires additional keywords to describe the layout of the data. Unfortunately the syntax of these required additional keywords is convoluted. Nevertheless the general binary mode is particularly useful for application programs sending large amounts of data to gnuplot. Syntax: plot '' {binary } ... splot '' {binary } ... General binary format is activated by keywords in pertaining to information about file structure, i.e., `array`, `record`, `format` or `filetype`. Otherwise, non-uniform matrix binary format is assumed. (See `binary matrix` for more details.) Gnuplot knows how to read a few standard binary file types that are fully self-describing, e.g. PNG images. Type `show datafile binary` at the command line for a list. Apart from these, you can think of binary data files as conceptually the same as text data. Each point has columns of information which are selected via the `using` specification. If no `format` string is specified, gnuplot will read in a number of binary values equal to the largest column given in the ``. For example, `using 1:3` will result in three columns being read, of which the second will be ignored. Certain plot types have an associated default using specification. For example, `with image` has a default of `using 1`, while `with rgbimage` has a default of `using 1:2:3`. 4 array ?binary array Describes the sampling array dimensions associated with the binary file. The coordinates will be generated by gnuplot. A number must be specified for each dimension of the array. For example, `array=(10,20)` means the underlying sampling structure is two-dimensional with 10 points along the first (x) dimension and 20 points along the second (y) dimension. A negative number indicates that data should be read until the end of file. If there is only one dimension, the parentheses may be omitted. A colon can be used to separate the dimensions for multiple records. For example, `array=25:35` indicates there are two one-dimensional records in the file. 4 record ?binary record This keyword serves the same function as `array` and has the same syntax. However, `record` causes gnuplot to not generate coordinate information. This is for the case where such information may be included in one of the columns of the binary data file. 4 skip ?binary skip This keyword allows you to skip sections of a binary file. For instance, if the file contains a 1024 byte header before the start of the data region you would probably want to use plot '' binary skip=1024 ... If there are multiple records in the file, you may specify a leading offset for each. For example, to skip 512 bytes before the 1st record and 256 bytes before the second and third records plot ' binary record=356:356:356 skip=512:256:256 ... 4 format ?binary format The default binary format is a float. For more flexibility, the format can include details about variable sizes. For example, `format="%uchar%int%float"` associates an unsigned character with the first using column, an int with the second column and a float with the third column. If the number of size specifications is less than the greatest column number, the size is implicitly taken to be similar to the last given variable size. Furthermore, similar to the `using` specification, the format can include discarded columns via the `*` character and have implicit repetition via a numerical repeat-field. For example, `format="%*2int%3float"` causes gnuplot to discard two ints before reading three floats. To list variable sizes, type `show datafile binary datasizes`. There are a group of names that are machine dependent along with their sizes in bytes for the particular compilation. There is also a group of names which attempt to be machine independent. 4 endian ?binary endian Often the endianess of binary data in the file does not agree with the endianess used by the platform on which gnuplot is running. Several words can direct gnuplot how to arrange bytes. For example `endian=little` means treat the binary file as having byte significance from least to greatest. The options are little: least significant to greatest significance big: greatest significance to least significance default: assume file endianess is the same as compiler swap (swab): Interchange the significance. (If things don't look right, try this.) Gnuplot can support "middle" ("pdp") endian if it is compiled with that option. 4 filetype ?binary filetype ?filetype For some standard binary file formats gnuplot can extract all the necessary information from the file in question. As an example, "format=edf" will read ESRF Header File format files. For a list of the currently supported file formats, type `show datafile binary filetypes`. There is a special file type called `auto` for which gnuplot will check if the binary file's extension is a quasi-standard extension for a supported format. Command line keywords may be used to override settings extracted from the file. The settings from the file override any defaults. See `set datafile binary`. 5 avs ?binary filetype avs ?filetype avs ?avs `avs` is one of the automatically recognized binary file types for images. AVS is an extremely simple format, suitable mostly for streaming between applications. It consists of 2 longs (xwidth, ywidth) followed by a stream of pixels, each with four bytes of information alpha/red/green/blue. 5 edf ?binary filetype edf ?filetype edf ?edf ?filetype ehf ?ehf `edf` is one of the automatically recognized binary file types for images. EDF stands for ESRF Data Format, and it supports both edf and ehf formats (the latter means ESRF Header Format). More information on specifications can be found at http://www.edfplus.info/specs 5 png ?binary filetype png ?binary filetype gif ?binary filetype jpeg ?filetype png ?filetype gif ?filetype jpeg If gnuplot was configured to use the libgd library for png/gif/jpeg output, then it can also be used to read these same image types as binary files. You can use an explicit command plot 'file.png' binary filetype=png Or the file type will be recognized automatically from the extension if you have previously requested set datafile binary filetype=auto 4 keywords ?binary keywords The following keywords apply only when generating coordinates from binary data files. That is, the control mapping the individual elements of a binary array, matrix, or image to specific x/y/z positions. 5 scan ?binary keywords scan ?scan A great deal of confusion can arise concerning the relationship between how gnuplot scans a binary file and the dimensions seen on the plot. To lessen the confusion, conceptually think of gnuplot _always_ scanning the binary file point/line/plane or fast/medium/slow. Then this keyword is used to tell gnuplot how to map this scanning convention to the Cartesian convention shown in plots, i.e., x/y/z. The qualifier for scan is a two or three letter code representing where point is assigned (first letter), line is assigned (second letter), and plane is assigned (third letter). For example, `scan=yx` means the fastest, point-by-point, increment should be mapped along the Cartesian y dimension and the middle, line-by-line, increment should be mapped along the x dimension. When the plotting mode is `plot`, the qualifier code can include the two letters x and y. For `splot`, it can include the three letters x, y and z. There is nothing restricting the inherent mapping from point/line/plane to apply only to Cartesian coordinates. For this reason there are cylindrical coordinate synonyms for the qualifier codes where t (theta), r and z are analogous to the x, y and z of Cartesian coordinates. 5 transpose ?binary keywords transpose ?transpose Shorthand notation for `scan=yx` or `scan=yxz`. I.e. it affects the assignment of pixels to scan lines during input. To instead transpose an image when it is displayed try plot 'imagefile' binary filetype=auto flipx rotate=90deg with rgbimage 5 dx, dy, dz ?binary keywords dx ?binary keywords dy ?dx ?dy When gnuplot generates coordinates, it uses the spacing described by these keywords. For example `dx=10 dy=20` would mean space samples along the x dimension by 10 and space samples along the y dimension by 20. `dy` cannot appear if `dx` does not appear. Similarly, `dz` cannot appear if `dy` does not appear. If the underlying dimensions are greater than the keywords specified, the spacing of the highest dimension given is extended to the other dimensions. For example, if an image is being read from a file and only `dx=3.5` is given gnuplot uses a delta x and delta y of 3.5. The following keywords also apply only when generating coordinates. However they may also be used with matrix binary files. 5 flipx, flipy, flipz ?binary keywords flipx ?flipx ?flipy ?flipz Sometimes the scanning directions in a binary datafile are not consistent with that assumed by gnuplot. These keywords can flip the scanning direction along dimensions x, y, z. 5 origin ?binary keywords origin ?binary origin When gnuplot generates coordinates based upon transposition and flip, it attempts to always position the lower left point in the array at the origin, i.e., the data lies in the first quadrant of a Cartesian system after transpose and flip. To position the array somewhere else on the graph, the `origin` keyword directs gnuplot to position the lower left point of the array at a point specified by a tuple. The tuple should be a double for `plot` and a triple for `splot`. For example, `origin=(100,100):(100,200)` is for two records in the file and intended for plotting in two dimensions. A second example, `origin=(0,0,3.5)`, is for plotting in three dimensions. 5 center ?binary keywords center ?keywords center ?center Similar to `origin`, this keyword will position the array such that its center lies at the point given by the tuple. For example, `center=(0,0)`. Center does not apply when the size of the array is `Inf`. 5 rotate ?binary keywords rotate ?keywords rotate ?rotate The transpose and flip commands provide some flexibility in generating and orienting coordinates. However, for full degrees of freedom, it is possible to apply a rotational vector described by a rotational angle in two dimensions. The `rotate` keyword applies to the two-dimensional plane, whether it be `plot` or `splot`. The rotation is done with respect to the positive angle of the Cartesian plane. The angle can be expressed in radians, radians as a multiple of pi, or degrees. For example, `rotate=1.5708`, `rotate=0.5pi` and `rotate=90deg` are equivalent. If `origin` is specified, the rotation is done about the lower left sample point before translation. Otherwise, the rotation is done about the array `center`. 5 perpendicular ?binary keywords perpendicular ?perpendicular For `splot`, the concept of a rotational vector is implemented by a triple representing the vector to be oriented normal to the two-dimensional x-y plane. Naturally, the default is (0,0,1). Thus specifying both rotate and perpendicular together can orient data myriad ways in three-space. The two-dimensional rotation is done first, followed by the three-dimensional rotation. That is, if R' is the rotational 2 x 2 matrix described by an angle, and P is the 3 x 3 matrix projecting (0,0,1) to (xp,yp,zp), let R be constructed from R' at the upper left sub-matrix, 1 at element 3,3 and zeros elsewhere. Then the matrix formula for translating data is v' = P R v, where v is the 3 x 1 vector of data extracted from the data file. In cases where the data of the file is inherently not three-dimensional, logical rules are used to place the data in three-space. (E.g., usually setting the z-dimension value to zero and placing 2D data in the x-y plane.) 3 data ?commands plot datafile ?plot datafile ?data-file ?datafile ?data ?file Data provided in a file can be plotted by giving the name of the file (enclosed in single or double quotes) on the `plot` command line. Data may also come from an input stream that is not a file. See `special-filenames`, `piped-data`, `datablocks`. Syntax: plot '' {binary } {{nonuniform|sparse} matrix} {index | index ""} {every } {skip } {using } {convexhull} {concavehull} {smooth
3 arrow ?commands set arrow ?commands unset arrow ?commands show arrow ?set arrow ?unset arrow ?show arrow ?arrow ?noarrow Arbitrary arrows can be placed on a plot using the `set arrow` command. Syntax: set arrow {} from to set arrow {} from rto set arrow {} from length angle set arrow arrowstyle | as set arrow {nohead | head | backhead | heads} {size ,{,}} {fixed} {filled | empty | nofilled | noborder} {front | back} {linestyle | ls } {linetype | lt } {linewidth | lw } {linecolor | lc } {dashtype | dt } unset arrow {} show arrow {} is an integer that identifies the arrow. If no tag is given, the lowest unused tag value is assigned automatically. The tag can be used to delete or change a specific arrow. To change any attribute of an existing arrow, use `set arrow` with the appropriate tag and specify the attributes to be changed. The position of the first end point of the arrow is always specified by "from". The other end point can be specified using any of three different mechanisms. The s are specified by either x,y or x,y,z, and may be preceded by `first`, `second`, `graph`, `screen`, or `character` to select the coordinate system. Unspecified coordinates default to 0. See `coordinates` for details. A coordinate system specifier does not carry over from the first endpoint description the second. 1) "to " specifies the absolute coordinates of the other end. 2) "rto " specifies an offset to the "from" position. For linear axes, `graph` and `screen` coordinates, the distance between the start and the end point corresponds to the given relative coordinate. For logarithmic axes, the relative given coordinate corresponds to the factor of the coordinate between start and end point. Thus, a negative relative value or zero are not allowed for logarithmic axes. 3) "length angle " specifies the orientation of the arrow in the plane of the graph. Again any of the coordinate systems can be used to specify the length. The angle is always in degrees. Other characteristics of the arrow can either be specified as a pre-defined arrow style or by providing them in `set arrow` command. For a detailed explanation of arrow characteristics, see `arrowstyle`. Examples: To set an arrow pointing from the origin to (1,2) with user-defined linestyle 5, use: set arrow to 1,2 ls 5 To set an arrow from bottom left of plotting area to (-5,5,3), and tag the arrow number 3, use: set arrow 3 from graph 0,0 to -5,5,3 To change the preceding arrow to end at 1,1,1, without an arrow head and double its width, use: set arrow 3 to 1,1,1 nohead lw 2 To draw a vertical line from the bottom to the top of the graph at x=3, use: set arrow from 3, graph 0 to 3, graph 1 nohead To draw a vertical arrow with T-shape ends, use: set arrow 3 from 0,-5 to 0,5 heads size screen 0.1,90 To draw an arrow relatively to the start point, where the relative distances are given in graph coordinates, use: set arrow from 0,-5 rto graph 0.1,0.1 To draw an arrow with relative end point in logarithmic x axis, use: set logscale x set arrow from 100,-5 rto 10,10 This draws an arrow from 100,-5 to 1000,5. For the logarithmic x axis, the relative coordinate 10 means "factor 10" while for the linear y axis, the relative coordinate 10 means "difference 10". To delete arrow number 2, use: unset arrow 2 To delete all arrows, use: unset arrow To show all arrows (in tag order), use: show arrow ^ arrows demos. ^ 3 autoscale ?commands set autoscale ?commands unset autoscale ?commands show autoscale ?set autoscale ?unset autoscale ?show autoscale ?autoscale ?noautoscale Autoscaling may be set individually on the x, y or z axis or globally on all axes. The default is to autoscale all axes. If you want to autoscale based on a subset of the plots in the figure, you can mark the ones to be omitted with the flag `noautoscale` in the plot command. See `datafile`. Syntax: set autoscale {{|min|max|fixmin|fixmax|fix} | fix | keepfix} set autoscale noextend unset autoscale {} show autoscale where is `x`, `y`, `z`, `cb`, `x2`, `y2`, `xy`, or `paxis
`. Appending `min` or `max` to the axis name tells `gnuplot` to autoscale only the minimum or maximum of that axis. If no axis name is given, all axes are autoscaled. Autoscaling the independent axes (x for `plot` and x,y for `splot`) adjusts the axis range to match the data being plotted. If the plot contains only functions (no input data), autoscaling these axes has no effect. Autoscaling the dependent axis (y for a `plot` and z for `splot`) adjusts the axis range to match the data or function being plotted. Adjustment of the axis range includes extending it to the next tic mark; i.e. unless the extreme data coordinate exactly matches a tic mark, there will be some blank space between the data and the plot border. Addition of this extra space can be suppressed by `noextend`. It can be further increased by the command `set offset`. Please see `set xrange` and `set offsets` for additional information. The behavior of autoscaling remains consistent in parametric mode, (see `set parametric`). However, there are more dependent variables and hence more control over x, y, and z axis scales. In parametric mode, the independent or dummy variable is t for `plot`s and u,v for `splot`s. `autoscale` in parametric mode, then, controls all ranges (t, u, v, x, y, and z) and allows x, y, and z to be fully autoscaled. When tics are displayed on second axes but no plot has been specified for those axes, x2range and y2range are inherited from xrange and yrange. This is done _before_ applying offsets or autoextending the ranges to a whole number of tics, which can cause unexpected results. To prevent this you can explicitly link the secondary axis range to the primary axis range. See `set link`. 4 noextend ?set autoscale noextend ?set autoscale keepfix ?set autoscale fix ?autoscale noextend ?noextend ?keepfix ?fix set autoscale noextend By default autoscaling sets the axis range limits to the nearest tic label position that includes all the plot data. Keywords `fixmin`, `fixmax`, `fix` or `noextend` tell gnuplot to disable extension of the axis range to the next tic mark position. In this case the axis range limit exactly matches the coordinate of the most extreme data point. `set autoscale noextend` is a synonym for `set autoscale fix`. Range extension for a single axis can be disabled by appending the `noextend` keyword to the corresponding range command, e.g. set yrange [0:*] noextend `set autoscale keepfix` autoscales all axes while leaving the fix settings unchanged. 4 examples ?autoscale examples ?set autoscale examples Examples: This sets autoscaling of the y axis (other axes are not affected): set autoscale y This sets autoscaling only for the minimum of the y axis (the maximum of the y axis and the other axes are not affected): set autoscale ymin This disables extension of the x2 axis tics to the next tic mark, thus keeping the exact range as found in the plotted data and functions: set autoscale x2fixmin set autoscale x2fixmax This sets autoscaling of the x and y axes: set autoscale xy This sets autoscaling of the x, y, z, x2 and y2 axes: set autoscale This disables autoscaling of the x, y, z, x2 and y2 axes: unset autoscale This disables autoscaling of the z axis only: unset autoscale z 4 polar mode ?commands set autoscale polar ?set autoscale polar When in polar mode (`set polar`), the xrange and the yrange may be left in autoscale mode. If `set rrange` is used to limit the extent of the polar axis, then xrange and yrange will adjust to match this automatically. However, explicit xrange and yrange commands can later be used to make further adjustments. See `set rrange`. See also ^ polar demos. ^ 3 bind ?commands show bind ?show bind =bind `show bind` shows the current state of all hotkey bindings. See `bind`. 3 bmargin ?commands set bmargin ?set bmargin ?bmargin The command `set bmargin` sets the size of the bottom margin. Please see `set margin` for details. 3 border ?commands set border ?commands unset border ?commands show border ?set border ?set border polar ?unset border ?show border ?border ?noborder The `set border` and `unset border` commands control the display of the graph borders for the `plot` and `splot` commands. Note that the borders do not necessarily coincide with the axes; with `plot` they often do, but with `splot` they usually do not. Syntax: set border {} {front | back | behind} {linestyle | ls } {linetype | lt } {linewidth | lw } {linecolor | lc } {dashtype | dt } {polar} unset border show border With a `splot` displayed in an arbitrary orientation, like `set view 56,103`, the four corners of the x-y plane can be referred to as "front", "back", "left" and "right". A similar set of four corners exist for the top surface, of course. Thus the border connecting, say, the back and right corners of the x-y plane is the "bottom right back" border, and the border connecting the top and bottom front corners is the "front vertical". (This nomenclature is defined solely to allow the reader to figure out the table that follows.) The borders are encoded in a 12-bit integer: the four low bits control the border for `plot` and the sides of the base for `splot`; the next four bits control the verticals in `splot`; the four high bits control the edges on top of an `splot`. The border settings is thus the sum of the appropriate entries from the following table: @start table - first is interactive cleartext form Bit plot splot 1 bottom bottom left front 2 left bottom left back 4 top bottom right front 8 right bottom right back 16 no effect left vertical 32 no effect back vertical 64 no effect right vertical 128 no effect front vertical 256 no effect top left back 512 no effect top right back 1024 no effect top left front 2048 no effect top right front 4096 polar no effect #\begin{tabular}{|c|c|c|} \hline #\multicolumn{3}{|c|}{Graph Border Encoding} \\ \hline \hline # Bit & plot & splot \\ \hline # 1 & bottom & bottom left front \\ # 2 & left & bottom left back \\ # 4 & top & bottom right front \\ # 8 & right & bottom right back \\ # 16 & no effect & left vertical \\ # 32 & no effect & back vertical \\ # 64 & no effect & right vertical \\ # 128 & no effect & front vertical \\ # 256 & no effect & top left back \\ # 512 & no effect & top right back \\ # 1024 & no effect & top left front \\ # 2048 & no effect & top right front \\ # 4096 & polar & no effect \\ %c c c . %Bit@plot@splot %_ %1@bottom@bottom left front %2@left@bottom left back %4@top@bottom right front %8@right@bottom right back %16@no effect@left vertical %32@no effect@back vertical %64@no effect@right vertical %128@no effect@front vertical %256@no effect@top left back %512@no effect@top right back %1024@no effect@top left front %2048@no effect@top right front %4096@polar@no effect @end table ^ ^^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^

Bit plot splot
1 bottom bottom left front
2 left bottom left back
4 top bottom right front
8 right bottom right back
16 no effect left vertical
32 no effect back vertical
64 no effect right vertical
128 no effect front vertical
256 no effect top left back
512 no effect top right back
1024 no effect top left front
2048 no effect top right front
4096 polar no effect
The default setting is 31, which is all four sides for `plot`, and base and z axis for `splot`. Separate from the four vertical lines in a 3D border, the `splot` command by default draws a vertical line each corner of a surface to the base plane of the plot. These verticals are not controlled by `set border`. Instead use `set/unset cornerpoles`. In 2D plots the border is normally drawn on top of all plots elements (`front`). If you want the border to be drawn behind the plot elements, use `set border back`. In hidden3d plots the lines making up the border are normally subject to the same hidden3d processing as the plot elements. `set border behind` will override this default. Using the optional , , , , and specifiers, the way the border lines are drawn can be influenced (limited by what the current terminal driver supports). Besides the border itself, this line style is used for the tics, independent of whether they are plotted on the border or on the axes (see `set xtics`). For `plot`, tics may be drawn on edges other than bottom and left by enabling the second axes -- see `set xtics` for details. If a `splot` draws only on the base, as is the case with "`unset surface; set contour base`", then the verticals and the top are not drawn even if they are specified. The `set grid` options 'back', 'front' and 'layerdefault' also control the order in which the border lines are drawn with respect to the output of the plotted data. The `polar` keyword enables a circular border for polar plots. Examples: Draw default borders: set border Draw only the left and bottom (`plot`) or both front and back bottom left (`splot`) borders: set border 3 Draw a complete box around a `splot`: set border 4095 Draw a topless box around a `splot`, omitting the front vertical: set border 127+256+512 # or set border 1023-128 Draw only the top and right borders for a `plot` and label them as axes: unset xtics; unset ytics; set x2tics; set y2tics; set border 12 3 boxwidth ?commands set boxwidth ?commands show boxwidth ?set boxwidth ?show boxwidth ?boxwidth The `set boxwidth` command is used to set the default width of boxes in the `boxes`, `boxerrorbars`, `boxplot`, `candlesticks` and `histograms` styles. Syntax: set boxwidth {} {absolute|relative} show boxwidth By default, adjacent boxes are extended in width until they touch each other. A different default width may be specified using the `set boxwidth` command. `Relative` widths are interpreted as being a fraction of this default width. An explicit value for the boxwidth is interpreted as being a number of units along the current x axis (`absolute`) unless the modifier `relative` is given. If the x axis is a log-scale (see `set log`) then the value of boxwidth is truly "absolute" only at x=1; this physical width is maintained everywhere along the axis (i.e. the boxes do not become narrower the value of x increases). If the range spanned by a log scale x axis is far from x=1, some experimentation may be required to find a useful value of boxwidth. The default is superseded by explicit width information taken from an extra data column in styles `boxes` or `boxerrorbars`. See `style boxes` and `style boxerrorbars` for more details. To set the box width to automatic use the command set boxwidth To set the box width to half of the automatic size use set boxwidth 0.5 relative To set the box width to an absolute value of 2 use set boxwidth 2 absolute 3 boxdepth ?commands set boxdepth ?commands show boxdepth ?set boxdepth ?show boxdepth ?boxdepth set boxdepth {} | square The `set boxdepth` command affects only 3D plots created by `splot with boxes`. It sets the extent of each box along the y axis, i.e. its thickness. `set boxdepth square` will try to choose a y extent that gives the appearance of a square cross section independent of the axis scales on x and y. 3 chi_shapes ?command set chi_shapes ?set chi_shapes ?command unset chi_shapes ?unset chi_shapes ?chi_shapes set chi_shapes fraction unset chi_shapes The concave hull filter creates Ï‡-shapes defined by a characteristic length chi_length. If no chi_length variable has been set, it chooses a value equal to a fraction of the longest edge in the bounding polygon (the convex hull). The fraction defaults to 0.6 but can be changed using this command. Choosing a value of 1.0 will reduce the resulting hull to the convex hull. Smaller values will produce increasingly concave hulls. See `concavehull`. The `unset chi_shapes` command restores the fraction to 0.6 and undefines the chi_length variable. 3 color ?commands set color ?set color Gnuplot assigns each element of a `plot` or `splot` command a new set of line properties taken from a predefined sequence. The default is to distinguish successive lines by a change in color. The alternative selected by `set monochrome` uses a sequence of black lines distinguished by linewidth or dot/dash pattern. The `set color` command exits this alternative monochrome mode and restores the previous set of default color lines. See `set monochrome`, `set linetype`, and `set colorsequence`. 3 colormap ?commands set colormap ?set colormap ?colormap ?show colormap =alpha channel =transparency =palette Syntax: set colormap new set colormap range [:] show colormaps `set colormap new ` creates a colormap array and loads it from the current palette settings. This saved colormap can be further manipulated as an array of 32-bit ARGB color values and used by name in subsequent plots. Here is an example that creates a palette running from dark red to white, saves it to a colormap array named 'Reds', and makes all entries in the colormap partially transparent. This named colormap is then used later to color a pm3d surface. Note that the alpha channel value in a named colormap follows the convention for ARGB line properties; i.e 0 is opaque, 0xff is fully transparent. set palette defined (0 "dark-red", 1 "white") set colormap new Reds do for [i=1:|Reds|] { Reds[i] = Reds[i] | 0x3F000000 } splot func(x,y) with pm3d fillcolor palette Reds The mapping of z values onto the colormap can be tuned by setting minimum and maximum z values that correspond to the end points. For example set colormap Reds range [0:10] If no range is set, or if min and max are the same, then the mapping uses the current limits of cbrange. See `set cbrange`. A colormap can be used to gradient-fill a rectangular area. See `pixmap colormap`. 3 colorsequence ?commands set colorsequence ?set colorsequence ?colorsequence Syntax: set colorsequence {default|classic|podo} `set colorsequence default` selects a terminal-independent repeating sequence of eight colors. See `set linetype`, `colors`. `set colorsequence classic` lets each separate terminal type provide its own sequence of line colors. The number provided varies from 4 to more than 100, but most start with red/green/blue/magenta/cyan/yellow. This was the default behaviour prior to version 5. `set colorsequence podo` selects eight colors drawn from a set recommended by Wong (2011) [Nature Methods 8:441] as being easily distinguished by color-blind viewers with either protanopia or deuteranopia. In each case you can further customize the length of the sequence and the colors used. See `set linetype`, `colors`. 3 clabel ?commands set clabel ?commands unset clabel ?commands show clabel ?set clabel ?unset clabel ?show clabel ?clabel This command has been deprecated. Use `set cntrlabel` instead. `set clabel "format"` is replaced by `set cntrlabel format "format"`. `unset clabel` is replaced by `set cntrlabel onecolor`. 3 clip ?commands set clip ?commands unset clip ?commands show clip ?set clip ?unset clip ?show clip ?clip Syntax: set clip {points|one|two|radial} unset clip {points|one|two|radial} show clip Default state: unset clip points set clip one unset clip two unset clip radial Data points whose center lies inside the plot boundaries are normally drawn even if the finite size of the point symbol causes it to extend past a boundary line. `set clip points` causes such points to be clipped (i.e. not drawn) even though the point center is inside the boundaries of a 2D plot. Data points whose center lies outside the plot boundaries are never drawn. `unset clip` causes a line segment in a plot not to be drawn if either end of that segment lies outside the plot boundaries (i.e. xrange and yrange). `set clip one` causes `gnuplot` to draw the in-range portion of line segments with one endpoint in range and one endpoint out of range. `set clip two` causes `gnuplot` to draw the in-range portion of line segments with both endpoints out of range. Line segments that lie entirely outside the plot boundaries are never drawn. `set clip radial` affects plotting only in polar mode. It clips lines against the radial bound established by `set rrange [0:MAX]`. This criteria is applied in conjunction with `set clip {one|two}`. I.e. the portion of a line between two points with R > RMAX that passes through the circle R = RMAX is drawn only if both `clip two` and `clip radial` are set. Notes: * `set clip` affects only points and lines produced by plot styles `lines`, `linespoints`, `points`, `arrows`, and `vectors`. * Clipping of colored quadrangles drawn for pm3d surfaces and other solid objects is controlled `set pm3d clipping`. The default is smooth clipping against the current zrange. * Object clipping is controlled by the `clip` or `noclip` property of the individual object. * In the current version of gnuplot, "plot with vectors" in polar mode does not test or clip against the maximum radius. 3 cntrlabel ?commands set cntrlabel ?commands show cntrlabel ?set cntrlabel ?show cntrlabel ?cntrlabel Syntax: set cntrlabel {format "format"} {font "font"} set cntrlabel {start } {interval } set cntrlabel onecolor `set cntrlabel` controls the labeling of contours, either in the key (default) or on the plot itself in the case of `splot ... with labels`. In the latter case labels are placed along each contour line according to the `pointinterval` or `pointnumber` property of the label descriptor. By default a label is placed on the 5th line segment making up the contour line and repeated every 20th segment. These defaults are equivalent to set cntrlabel start 5 interval 20 They can be changed either via the `set cntrlabel` command or by specifying the interval in the `splot` command itself set contours; splot $FOO with labels point pointinterval -1 Setting the interval to a negative value means that the label appear only once per contour line. However if `set samples` or `set isosamples` is large then many contour lines may be created, each with a single label. A contour label is placed in the plot key for each linetype used. By default each contour level is given its own linetype, so a separate label appears for each. The command `set cntrlabel onecolor` causes all contours to be drawn using the same linetype, so only one label appears in the plot key. This command replaces an older command `unset clabel`. 3 cntrparam ?commands set cntrparam ?commands show cntrparam ?set cntrparam ?show cntrparam ?cntrparam `set cntrparam` controls the generation of contours and their smoothness for a contour plot. `show contour` displays current settings of `cntrparam` as well as `contour`. Syntax: set cntrparam { { linear | cubicspline | bspline | points | order | levels { | auto {} | discrete {,{,...}} | incremental , {,} } {{un}sorted} {firstlinetype N} } } show contour This command has two functions. First, it sets the values of z for which contours are to be determined. The number of contour levels should be an integral constant expression. , ... are real-valued expressions. Second, it controls the appearance of the individual contour lines. Keywords controlling the smoothness of contour lines: `linear`, `cubicspline`, `bspline`--- Controls type of approximation or interpolation. If `linear`, then straight line segments connect points of equal z magnitude. If `cubicspline`, then piecewise-linear contours are interpolated between the same equal z points to form somewhat smoother contours, but which may undulate. If `bspline`, a guaranteed-smoother curve is drawn, which only approximates the position of the points of equal-z. `points`--- Eventually all drawings are done with piecewise-linear strokes. This number controls the number of line segments used to approximate the `bspline` or `cubicspline` curve. Number of cubicspline or bspline segments (strokes) = `points` * number of linear segments. `order`--- Order of the bspline approximation to be used. The bigger this order is, the smoother the resulting contour. (Of course, higher order bspline curves will move further away from the original piecewise linear data.) This option is relevant for `bspline` mode only. Allowed values are integers in the range from 2 (linear) to 10. Keywords controlling the selection of contour levels: `levels auto`--- This is the default. specifies a nominal number of levels; the actual number will be adjusted to give simple labels. If the surface is bounded by zmin and zmax, contours will be generated at integer multiples of dz between zmin and zmax, where dz is 1, 2, or 5 times some power of ten (like the step between two tic marks). `levels discrete`--- Contours will be generated at z = , ... as specified; the number of discrete levels sets the number of contour levels. In `discrete` mode, any `set cntrparam levels ` are ignored. `levels incremental`--- Contours are generated at values of z beginning at and increasing by , until the number of contours is reached. is used to determine the number of contour levels, which will be changed by any subsequent `set cntrparam levels `. If the z axis is logarithmic, will be interpreted as a multiplicative factor, as it is for `set ztics`, and should not be used. Keywords controlling the assignment of linetype to contours: By default the contours are generated in the reverse order specified (`unsorted`). Thus `set cntrparam levels increment 0, 10, 100` will create 11 contours levels starting with 100 and ending with 0. Adding the keyword `sorted` re-orders the contours by increasing numerical value, which in this case would mean the first contour is drawn at 0. By default contours are drawn using successive linetypes starting with the next linetype after that used for the corresponding surface. Thus `splot x*y lt 5` would use lt 6 for the first contour generated. If `hidden3d` mode is active then each surface uses two linetypes. In this case using default settings would cause the first contour to use the same linetype as the hidden surface, which is undesirable. This can be avoided in either of two ways. (1) Use `set hidden3d offset N` to change the linetype used for the hidden surface. A good choice would be `offset -1` since that will avoid all the contour linetypes. (2) Use the `set cntrparam firstlinetype N` option to specify a block of linetypes used for contour lines independent of whatever was used for the surface. This is particularly useful if you want to customize the set of contour linetypes. N <= 0 restores the default. If the command `set cntrparam` is given without any arguments specified all options are reset to the default: set cntrparam order 4 points 5 set cntrparam levels auto 5 unsorted set cntrparam firstlinetype 0 4 Examples ?commands set cntrparam examples ?set cntrparam examples ?cntrparam examples Examples: set cntrparam bspline set cntrparam points 7 set cntrparam order 10 To select levels automatically, 5 if the level increment criteria are met: set cntrparam levels auto 5 To specify discrete levels at .1, .37, and .9: set cntrparam levels discrete .1,1/exp(1),.9 To specify levels from 0 to 4 with increment 1: set cntrparam levels incremental 0,1,4 To set the number of levels to 10 (changing an incremental end or possibly the number of auto levels): set cntrparam levels 10 To set the start and increment while retaining the number of levels: set cntrparam levels incremental 100,50 To define and use a customized block of contour linetypes set linetype 100 lc "red" dt '....' do for [L=101:199] { if (L%10 == 0) { set linetype L lc "black" dt solid lw 2 } else { set linetype L lc "gray" dt solid lw 1 } } set cntrparam firstlinetype 100 set cntrparam sorted levels incremental 0, 1, 100 See also `set contour` for control of where the contours are drawn, and `set cntrlabel` for control of the format of the contour labels and linetypes. See also ^ contours demo (contours.dem) ^ and ^ contours with user defined levels demo (discrete.dem). ^ D contours 5 D discrete 3 3 color box ?commands set colorbox ?commands show colorbox ?commands unset colorbox ?set colorbox ?show colorbox ?unset colorbox ?colorbox For plots that use palette coloring, in particular pm3d plots, the palette gradient is drawn in a color box next to the plot unless it is switched off by `unset colorbox`. set colorbox set colorbox { { vertical | horizontal } {{no}invert} { default | bottom | user } { origin x, y } { size x, y } { front | back } { noborder | bdefault | border } } show colorbox unset colorbox The orientation of the color gradient is set by `vertical` or `horizontal`. The color box position can be `default` or `bottom` or `user`. The `bottom` keyword is a convenience short cut equivalent to set colorbox horizontal user origin screen 0.1, 0.07 size 0.8, 0.03. If the colorbox is placed underneath the plot, as it is with `bottom`, it may be useful to reserve additional space for it: `set bmargin screen 0.2`. `origin x, y` and `size x, y` are used to tailor the exact placement in `user` or `bottom` positioning. The x and y values are interpreted as screen coordinates by default, and this is the only legal option for 3D plots. 2D plots, including splot with `set view map`, allow any coordinate system. `back`/`front` control whether the color box is draw before or after the plot. `border` turns the border on (this is the default). `noborder` turns the border off. If an positive integer argument is given after `border`, it is used as a line style tag which is used for drawing the border, e.g.: set style line 2604 linetype -1 linewidth .4 set colorbox border 2604 will use line style `2604`, a thin line with the default border color (-1) for drawing the border. `bdefault` (which is the default) will use the default border line style for drawing the border of the color box. The axis of the color box is called `cb` and it is controlled by means of the usual axes commands, i.e. `set/unset/show` with `cbrange`, `[m]cbtics`, `format cb`, `grid [m]cb`, `cblabel`, and perhaps even `cbdata`, `[no]cbdtics`, `[no]cbmtics`. `set colorbox` without any parameter switches the position to default. `unset colorbox` resets the default parameters for the colorbox and switches the colorbox off. See also help for `set pm3d`, `set palette`, and `set style line`. 3 colornames ?colornames Ffigure_colornames Gnuplot knows a limited number of color names. You can use these to define the color range spanned by a pm3d palette, to assign a named color to a particular linetype or linestyle, or to define a gradient for the current color palette. Use the command `show colornames` to list the known color names together with their RGB component definitions. Examples: set style line 1 linecolor "sea-green" set palette defined (0 "dark-red", 1 "white") print sprintf("0x%06x", rgbcolor("dark-green")) 0x006400 3 contour ?commands set contour ?commands unset contour ?commands show contour ?set contour ?unset contour ?show contour ?contour ?contours ?nocontour `set contour` enables placement of contour lines on 3D surfaces. This option is available only for `splot`. It requires grid data, e.g. a file in which all the points for a single y-isoline are listed, then all the points for the next y-isoline, and so on. A single blank line (containing no characters other than blank spaces) separates one y-isoline from the next. see `grid_data` for more details. If the data is not already gridded, `set dgrid3d` can be used to first create and populate an appropriate grid. Syntax: set contour {base | surface | both} unset contour show contour The three options specify where to draw the contours: `base` draws the contours on the grid base where the x/ytics are placed, `surface` draws the contours on the surfaces themselves, and `both` draws the contours on both the base and the surface. If no option is provided, the default is `base`. See also `set cntrparam` for the parameters that affect the drawing of contours, and `set cntrlabel` for control of labeling of the contours. Note that this option places lines or labels without otherwise changing the appearance of the surface itself. If you want to recolor the surface so that the areas bounded by contour lines are assigned distinct colors, use instead the contourfill plot style. See `contourfill`. While `set contour` is in effect, `splot with
and ^ user defined contour levels (discrete.dem). ^ 3 cornerpoles ?command set cornerpoles ?set cornerpoles ?cornerpoles By default splot draws a vertical line from each corner of a 3D surface to the base plane. These vertical lines can be suppressed using `unset cornerpoles`. 3 contourfill ?commands set contourfill ?commands show contourfill ?set contourfill ?show contourfill The 3D plot style `with contourfill` slices a pm3d surface into sections delimited by a set of planes perpendicular to the z axis. The command `set contourfill` controls placement of these limiting planes and the colors assigned to the individual sections. Syntax: set contourfill auto N # split zrange evenly into N slices set contourfill ztics # slice at each z axis tick matching level set contourfill cbtics # slice at each cb axis tick matching level set contourfill {palette | firstlinetype N} The default is `set contourfill auto 5 palette`, which splits the current z range into five equal slices (6 bounding planes) and assigns each slice the palette mapped color of its midpoint z value. The options `ztics` or `cbtics` place split zrange by slicing at major axis tick (level 0) or minor tick (level 1) or tick at some other level set explicitly by the user. For example to slice specifically at z=2.5, z=7 and z=10 independent of the major and minor tics you could use the commands below. set ztics add ("floor" 2.5 3, "boundary X" 7 3, "ceiling" 10 3) set contourfill ztics 3 set ztics scale 1, 0.5, 0, 0, 0 If you do not want to use palette coloring for the sections, you can choose any arbitrary range of successive linetypes and assign them the desired color sequence. set for [i=101:110] linetype i lc mycolor[i] set contourfill firstlinetype 101 `set contourfill palette` restores palette coloring. D contourfill 3 3 dashtype ?commands set dashtype ?commands show dashtype ?set dashtype ?show dashtype The `set dashtype` command allows you to define a dash pattern that can then be referred to by its index. This is purely a convenience, as anywhere that would accept the dashtype by its numerical index would also accept an explicit dash pattern. Example: set dashtype 5 (2,4,2,6) # define or redefine dashtype number 5 plot f1(x) dt 5 # plot using the new dashtype plot f1(x) dt (2,4,2,6) # exactly the same plot as above set linetype 5 dt 5 # always use this dash pattern with linetype 5 set dashtype 66 "..-" # define a new dashtype using a string See also `dashtype`. D dashtypes 2 3 datafile ?set datafile ?show datafile The `set datafile` command options control interpretation of fields read from input data files by the `plot`, `splot`, and `fit` commands. Several options are currently implemented. The settings apply uniformly to all data files read by subsequent commands; however see `functionblocks` for a way to work around this if it is necessary to simultaneously handles files with conflicting formats. 4 set datafile columnheaders ?set datafile columnheaders =columnheaders The `set datafile columnheaders` command guarantees that the first row of input will be interpreted as column headers rather than as data values. It affects all input data sources to plot, splot, fit, and stats commands. If this setting is disabled by `unset datafile columnheaders`, the same effect is triggered on a per-file basis if there is an explicit columnheader() function in a using specifier or plot title associated with that file. See also `set key autotitle` and `columnheader`. 4 set datafile fortran ?set datafile fortran ?show datafile fortran ?fortran The `set datafile fortran` command enables a special check for values in the input file expressed as Fortran D or Q constants. This extra check slows down the input process, and should only be selected if you do in fact have datafiles containing Fortran D or Q constants. The option can be disabled again using `unset datafile fortran`. 4 set datafile nofpe_trap ?set datafile nofpe_trap ?fpe_trap ?nofpe_trap =floating point exceptions The `set datafile nofpe_trap` command tells gnuplot not to re-initialize a floating point exception handler before every expression evaluation used while reading data from an input file. This can significantly speed data input from very large files at the risk of program termination if a floating-point exception is generated. 4 set datafile missing ?set datafile missing ?show datafile missing ?set missing ?missing Syntax: set datafile missing "" set datafile missing NaN show datafile missing unset datafile The `set datafile missing` command tells `gnuplot` there is a special string used in input data files to denote a missing data entry. There is no default character for `missing`. Gnuplot makes a distinction between missing data and invalid data (e.g. "NaN", 1/0.). For example invalid data causes a gap in a line drawn through sequential data points; missing data does not. Non-numeric characters found in a numeric field will usually be interpreted as invalid rather than as a missing data point unless they happen to match the `missing` string. Conversely `set datafile missing NaN` causes all data or expressions evaluating to not-a-number (NaN) to be treated as missing data. See the ^ imageNaN demo. ^ The program notices a missing value flag in column N when the using specifier in a plot command directly refers to the column as `using N`, `using ($N)`, or `using (function($N))`. In these cases the expression, e.g. func($N), is not evaluated at all. The current gnuplot version also notices direct references of the form (column(N)), and it notices during evaluation if the expression depends even indirectly on a column value flagged "missing". In all these cases the program treats the entire input data line as if it were not present at all. However if an expression depends on a data value that is truly missing (e.g. an empty field in a csv file) it may not be caught by these checks. If it evaluates to NaN it will be treated as invalid data rather than as a missing data point. If you want to treat such invalid data the same as missing data, use the command `set datafile missing NaN`. 4 set datafile separator ?set datafile separator ?show datafile separator ?datafile separator ?separator The command `set datafile separator` tells `gnuplot` that data fields in subsequent input files are separated by a specific character rather than by whitespace. The most common use is to read in csv (comma-separated value) files written by spreadsheet or database programs. By default data fields are separated by whitespace. Syntax: set datafile separator {whitespace | tab | comma | ""} Examples: # Input file contains tab-separated fields set datafile separator "\t" # Input file contains comma-separated values fields set datafile separator comma # Input file contains fields separated by either * or | set datafile separator "*|" 4 set datafile commentschars ?set datafile commentschars ?commentschars The command `set datafile commentschars` specifies what characters can be used in a data file to begin comment lines. If the first non-blank character on a line is one of these characters then the rest of the data line is ignored. Default value of the string is "#!" on VMS and "#" otherwise. Syntax: set datafile commentschars {""} show datafile commentschars unset commentschars Then, the following line in a data file is completely ignored # 1 2 3 4 but the following 1 # 3 4 will be interpreted as garbage in the 2nd column followed by valid data in the 3rd and 4th columns. Example: set datafile commentschars "#!%" 4 set datafile binary ?set datafile binary The `set datafile binary` command is used to set the defaults when reading binary data files. The syntax matches precisely that used for commands `plot` and `splot`. See `binary matrix` and `binary general` for details about the keywords that can be present in . Syntax: set datafile binary show datafile binary show datafile unset datafile Examples: set datafile binary filetype=auto set datafile binary array=(512,512) format="%uchar" ?show datafile binary show datafile binary # list current settings 3 decimalsign ?commands set decimalsign ?commands show decimalsign ?commands unset decimalsign ?set decimalsign ?show decimalsign ?unset decimalsign ?decimalsign =locale The `set decimalsign` command selects a decimal sign for numbers printed into tic labels or `set label` strings. Syntax: set decimalsign { | locale {""}} unset decimalsign show decimalsign The argument is a string to be used in place of the usual decimal point. Typical choices include the period, '.', and the comma, ',', but others may be useful, too. If you omit the argument, the decimal separator is not modified from the usual default, which is a period. Unsetting decimalsign has the same effect as omitting . Example: Correct typesetting in most European countries requires: set decimalsign ',' Please note: If you set an explicit string, this affects only numbers that are printed using gnuplot's gprintf() formatting routine, including axis tics. It does not affect the format expected for input data, and it does not affect numbers printed with the sprintf() formatting routine. To change the behavior of both input and output formatting, instead use the form set decimalsign locale This instructs the program to use both input and output formats in accordance with the current setting of the LC_ALL, LC_NUMERIC, or LANG environmental variables. set decimalsign locale "foo" This instructs the program to format all input and output in accordance with locale "foo", which must be installed. If locale "foo" is not found then an error message is printed and the decimal sign setting is unchanged. On linux systems you can get a list of the locales installed on your machine by typing "locale -a". A typical linux locale string is of the form "sl_SI.UTF-8". A typical Windows locale string is of the form "Slovenian_Slovenia.1250" or "slovenian". Please note that interpretation of the locale settings is done by the C library at runtime. Older C libraries may offer only partial support for locale settings such as the thousands grouping separator character. set decimalsign locale; set decimalsign "." This sets all input and output to use whatever decimal sign is correct for the current locale, but over-rides this with an explicit '.' in numbers formatted using gnuplot's internal gprintf() function. 3 dgrid3d ?commands set dgrid3d ?commands unset dgrid3d ?commands show dgrid3d ?set dgrid3d ?unset dgrid3d ?show dgrid3d ?dgrid3d ?nodgrid3d =kdensity ?nogrid The `set dgrid3d` command enables and sets parameters for mapping non-grid data onto a grid. See `splot grid_data` for details about the grid data structure. Aside from its use in fitting 3D surfaces, this process can also be used to generate 2D heatmaps, where the 'z' value of each point contributes to a local weighted value. Syntax: set dgrid3d {} {,{}} splines set dgrid3d {} {,{}} qnorm {} set dgrid3d {} {,{}} {gauss | cauchy | exp | box | hann} {kdensity} {} {,} unset dgrid3d show dgrid3d By default `dgrid3d` is disabled. When enabled, 3D data points read from a file are treated as a scattered data set used to fit a gridded surface. The grid dimensions are derived from the bounding box of the scattered data subdivided by the row/col_size parameters from the `set dgrid3d` statement. The grid is equally spaced in x (rows) and in y (columns); the z values are computed as weighted averages or spline interpolations of the scattered points' z values. In other words, a regularly spaced grid is created and then a smooth approximation to the raw data is evaluated for each grid point. This surface is then plotted in place of the raw data. While dgrid3d mode is enabled, if you want to plot individual points or lines without using them to create a gridded surface you must append the keyword `nogrid` to the corresponding splot command. The number of columns defaults to the number of rows, which defaults to 10. Several algorithms are available to calculate the approximation from the raw data. Some of these algorithms can take additional parameters. These interpolations are such that the closer the data point is to a grid point, the more effect it has on that grid point. The `splines` algorithm calculates an interpolation based on thin plate splines. It does not take additional parameters. The `qnorm` algorithm calculates a weighted average of the input data at each grid point. Each data point is weighted by the inverse of its distance from the grid point raised to some power. The power is specified as an optional integer parameter that defaults to 1. This algorithm is the default. Finally, several smoothing kernels are available to calculate weighted averages: z = Sum_i w(d_i) * z_i / Sum_i w(d_i), where z_i is the value of the i-th data point and d_i is the distance between the current grid point and the location of the i-th data point. All kernels assign higher weights to data points that are close to the current grid point and lower weights to data points further away. The following kernels are available: gauss : w(d) = exp(-d*d) cauchy : w(d) = 1/(1 + d*d) exp : w(d) = exp(-d) box : w(d) = 1 if d<1 = 0 otherwise hann : w(d) = 0.5*(1+cos(pi*d)) if d<1 w(d) = 0 otherwise When using one of these five smoothing kernels, up to two additional numerical parameters can be specified: dx and dy. These are used to rescale the coordinate differences when calculating the distance: d_i = sqrt( ((x-x_i)/dx)**2 + ((y-y_i)/dy)**2 ), where x,y are the coordinates of the current grid point and x_i,y_i are the coordinates of the i-th data point. The value of dy defaults to the value of dx, which defaults to 1. The parameters dx and dy make it possible to control the radius over which data points contribute to a grid point IN THE UNITS OF THE DATA ITSELF. The optional keyword `kdensity`, which must come after the name of the kernel, but before the optional scale parameters, modifies the algorithm so that the values calculated for the grid points are not divided by the sum of the weights ( z = Sum_i w(d_i) * z_i ). If all z_i are constant, this effectively plots a bivariate kernel density estimate: a kernel function (one of the five defined above) is placed at each data point, the sum of these kernels is evaluated at every grid point, and this smooth surface is plotted instead of the original data. This is similar in principle to what the `smooth kdensity` option does to 1D datasets. See kdensity2d.dem and heatmap_points.dem for usage example. Ffigure_dgrid3d The `dgrid3d` option is a simple scheme which replaces scattered data with weighted averages on a regular grid. More sophisticated approaches to this problem exist and should be used to preprocess the data outside `gnuplot` if this simple solution is found inadequate. See also the online demos for ^ dgrid3d ^ ^ scatter ^ and ^ heatmap_points ^ D heatmap_points 1 D heatmap_points 2 D heatmap_points 3 3 dummy ?commands set dummy ?commands show dummy ?set dummy ?show dummy ?unset dummy ?dummy The `set dummy` command changes the default dummy variable names. Syntax: set dummy {} {,} show dummy By default, `gnuplot` assumes that the independent, or "dummy", variable for the `plot` command is "t" if in parametric or polar mode, or "x" otherwise. Similarly the independent variables for the `splot` command are "u" and "v" in parametric mode (`splot` cannot be used in polar mode), or "x" and "y" otherwise. It may be more convenient to call a dummy variable by a more physically meaningful or conventional name. For example, when plotting time functions: set dummy t plot sin(t), cos(t) Examples: set dummy u,v set dummy ,s The second example sets the second variable to s. To reset the dummy variable names to their default values, use unset dummy 3 encoding ?commands set encoding ?commands show encoding ?set encoding ?show encoding ?encoding ?encodings ?utf8 ?sjis =UTF-8 =SJIS The `set encoding` command selects a character encoding. Syntax: set encoding {} set encoding locale show encoding Valid values are default - tells a terminal to use its default encoding iso_8859_1 - the most common Western European encoding prior to UTF-8. Known in the PostScript world as 'ISO-Latin1'. iso_8859_15 - a variant of iso_8859_1 that includes the Euro symbol iso_8859_2 - used in Central and Eastern Europe iso_8859_9 - used in Turkey (also known as Latin5) koi8r - popular Unix cyrillic encoding koi8u - Ukrainian Unix cyrillic encoding cp437 - codepage for MS-DOS cp850 - codepage for OS/2, Western Europe cp852 - codepage for OS/2, Central and Eastern Europe cp950 - MS version of Big5 (emf terminal only) cp1250 - codepage for MS Windows, Central and Eastern Europe cp1251 - codepage for 8-bit Russian, Serbian, Bulgarian, Macedonian cp1252 - codepage for MS Windows, Western Europe cp1254 - codepage for MS Windows, Turkish (superset of Latin5) sjis - shift-JIS Japanese encoding utf8 - variable-length (multibyte) representation of Unicode entry point for each character The command `set encoding locale` is different from the other options. It attempts to determine the current locale from the runtime environment. On most systems this is controlled by the environmental variables LC_ALL, LC_CTYPE, or LANG. This mechanism is necessary, for example, to pass multibyte character encodings such as UTF-8 or EUC_JP to the wxt and pdf terminals. This command does not affect the locale-specific representation of dates or numbers. See also `set locale` and `set decimalsign`. Generally you should set the encoding before setting the terminal type, as it may affect the selection of fonts. 3 errorbars ?commands set errorbars ?commands show errorbars ?set errorbars ?show errorbars ?errorbars ?commands set bars ?commands show bars ?set bars ?show bars ?bars The `set errorbars` command controls the tics at the ends of error bars, and also at the end of the whiskers belonging to a boxplot. Syntax: set errorbars {small | large | fullwidth | } {front | back} {line-properties} unset errorbars show errorbars `small` is a synonym for 0.0 (no crossbar), and `large` for 1.0. The default is 1.0 if no size is given. The keyword `fullwidth` is relevant only to boxplots and to histograms with errorbars. It sets the width of the errorbar ends to be the same as the width of the associated box. It does not change the width of the box itself. The `front` and `back` keywords are relevant only to errorbars attached to filled rectangles (boxes, candlesticks, histograms). Error bars are by default drawn using the same line properties as the border of the associated box. You can change this by providing a separate set of line properties for the error bars. set errorbars linecolor black linewidth 0.5 dashtype '.' 3 fit ?commands set fit ?commands show fit ?set fit ?show fit ?set fit quiet ?set fit verbose ?set fit brief ?set fit results ?set fit prescale ?set fit limit ?set fit maxiter ?set fit errorscaling ?set fit errorvariables ?set fit logfile ?set fit script ?set fit v4 ?set fit v5 The `set fit` command controls the options for the `fit` command. Syntax: set fit {nolog | logfile {""|default}} {{no}quiet|results|brief|verbose} {{no}errorvariables} {{no}covariancevariables} {{no}errorscaling} {{no}prescale} {maxiter |default} {limit |default} {limit_abs } {start-lambda |default} {lambda-factor |default} {script {""|default}} {v4 | v5} unset fit show fit The `logfile` option defines where the `fit` command writes its output. The argument must be enclosed in single or double quotes. If no filename is given or `unset fit` is used the log file is reset to its default value "fit.log" or the value of the environmental variable `FIT_LOG`. If the given logfile name ends with a / or \, it is interpreted to be a directory name, and the actual filename will be "fit.log" in that directory. By default the information written to the log file is also echoed to the terminal session. `set fit quiet` turns off the echo, whereas `results` prints only final results. `brief` gives one line summaries for every iteration of the fit in addition. `verbose` yields detailed iteration reports as in version 4. If the `errorvariables` option is turned on, the error of each fitted parameter computed by `fit` will be copied to a user-defined variable whose name is formed by appending "_err" to the name of the parameter itself. This is useful mainly to put the parameter and its error onto a plot of the data and the fitted function, for reference, as in: set fit errorvariables fit f(x) 'datafile' using 1:2 via a, b print "error of a is:", a_err set label 1 sprintf("a=%6.2f +/- %6.2f", a, a_err) plot 'datafile' using 1:2, f(x) If the `errorscaling` option is specified, which is the default, the calculated parameter errors are scaled with the reduced chi square. This is equivalent to providing data errors equal to the calculated standard deviation of the fit (FIT_STDFIT) resulting in a reduced chi square of one. With the `noerrorscaling` option the estimated errors are the unscaled standard deviations of the fit parameters. If no weights are specified for the data, parameter errors are always scaled. If the `prescale` option is turned on, parameters are prescaled by their initial values before being passed to the Marquardt-Levenberg routine. This helps tremendously if there are parameters that differ in size by many orders of magnitude. Fit parameters with an initial value of exactly zero are never prescaled. The maximum number of iterations may be limited with the `maxiter` option. A value of 0 or `default` means that there is no limit. The `limit` option can be used to change the default epsilon limit (1e-5) to detect convergence. When the sum of squared residuals changes by a factor less than this number (epsilon), the fit is considered to have 'converged'. The `limit_abs` option imposes an additional absolute limit in the change of the sum of squared residuals and defaults to zero. If you need even more control about the algorithm, and know the Marquardt-Levenberg algorithm well, the following options can be used to influence it. The startup value of `lambda` is normally calculated automatically from the ML-matrix, but if you want to, you may provide your own using the `start_lambda` option. Setting it to `default` will re-enable the automatic selection. The option `lambda_factor` sets the factor by which `lambda` is increased or decreased whenever the chi-squared target function increased or decreased significantly. Setting it to `default` re-enables the default factor of 10.0. The `script` option may be used to specify a `gnuplot` command to be executed when a fit is interrupted---see `fit`. This setting takes precedence over the default of `replot` and the environment variable `FIT_SCRIPT`. If the `covariancevariables` option is turned on, the covariances between final parameters will be saved to user-defined variables. The variable name for a certain parameter combination is formed by prepending "FIT_COV_" to the name of the first parameter and combining the two parameter names by "_". For example given the parameters "a" and "b" the covariance variable is named "FIT_COV_a_b". In version 5 the syntax of the fit command changed and it now defaults to unitweights if no 'error' keyword is given. The `v4` option restores the default behavior of gnuplot version 4, see also `fit`. 3 fontpath ?commands set fontpath ?commands show fontpath ?set fontpath ?show fontpath ?fontpath Syntax: set fontpath "/directory/where/my/fonts/live" set term postscript fontfile [DEPRECATED in version 5.4] The `fontpath` directory is relevant only for embedding fonts in postscript output produced by the postscript terminal. It has no effect on other gnuplot terminals. If you are not embedding fonts you do not need this command, and even if you are embedding fonts you only need it for fonts that cannot be found via the other paths below. Earlier versions of gnuplot tried to emulate a font manager by tracking multiple directory trees containing fonts. This is now replaced by a search in the following places: (1) an absolute path given in the `set term postscript fontfile` command (2) the current directory (3) any of the directories specified by `set loadpath` (4) the directory specified by `set fontpath` (5) the directory provided in environmental variable GNUPLOT_FONTPATH Note: The search path for fonts specified by filename for the libgd terminals (png gif jpeg sixel) is controlled by environmental variable GDFONTPATH. 3 format ?commands set format ?commands show format ?set format ?show format ?format ?format cb The format of the tic-mark labels can be set with the `set format` command or with the `set tics format` or individual `set {axis}tics format` commands. For information on using an explicit format for input data see `using format`. Syntax: set format {} {""} {numeric|timedate|geographic} show format where is either `x`, `y`, `xy`, `x2`, `y2`, `z`, `cb` or nothing (which applies the format to all axes). The following two commands are equivalent: set format y "%.2f" set ytics format "%.2f" The length of the string is restricted to 100 characters. The default format is "% h", "$%h$" for LaTeX terminals. Other formats such as "%.2f" or "%3.0em" are often desirable. "set format" with no following string will restore the default. If the empty string "" is given, tics will have no labels, although the tic mark will still be plotted. To eliminate the tic marks, use `unset xtics` or `set tics scale 0`. Newline (\n) and enhanced text markup is accepted in the format string. Use double-quotes rather than single-quotes in this case. See also `syntax`. Characters not preceded by "%" are printed verbatim. Thus you can include spaces and labels in your format string, such as "%g m", which will put " m" after each number. If you want "%" itself, double it: "%g %%". See also `set xtics` for more information about tic labels, and `set decimalsign` for how to use non-default decimal separators in numbers printed this way. See also ^ electron demo (electron.dem). ^ 4 gprintf ?gprintf The string function gprintf("format",x) uses gnuplot's own format specifiers, as do the gnuplot commands `set format`, `set timestamp`, and others. These format specifiers are not the same as those used by the standard C-language routine sprintf(). gprintf() accepts only a single variable to be formatted. Gnuplot also provides an sprintf("format",x1,x2,...) routine if you prefer. For a list of gnuplot's format options, see `format specifiers`. 4 format specifiers ?commands set format specifiers ?set format specifiers ?format specifiers ?format_specifiers The acceptable formats (if not in time/date mode) are: @start table - first is interactive cleartext form Format Explanation %f floating point notation %e or %E exponential notation; an "e" or "E" before the power %g or %G the shorter of %e (or %E) and %f %h or %H like %g with "x10^{%S}" or "*10^{%S}" instead of "e%S" %x or %X hex %o or %O octal %t mantissa to base 10 %l mantissa to base of current logscale %s mantissa to base of current logscale; scientific power %T power to base 10 %L power to base of current logscale %S scientific power %c character replacement for scientific power %b mantissa of ISO/IEC 80000 notation (ki, Mi, Gi, Ti, Pi, Ei, Zi, Yi) %B prefix of ISO/IEC 80000 notation (ki, Mi, Gi, Ti, Pi, Ei, Zi, Yi) %P multiple of pi #\begin{tabular}{|cl|} \hline #\multicolumn{2}{|c|}{Tic-mark label numerical format specifiers}\\ #\hline \hline #Format & Explanation \\ \hline #\verb@%f@ & floating point notation \\ #\verb@%e@ or \verb@%E@ & exponential notation; an "e" or "E" before the power \\ #\verb@%g@ or \verb@%G@ & the shorter of \verb@%e@ (or \verb@%E@) and \verb@%f@ \\ #\verb@%h@ or \verb@%H@ & like \verb@%g with "x10^{%S}" or "*10^{%S}" instead of "e%S"@ \\ #\verb@%x@ or \verb@%X@ & hex \\ #\verb@%o@ or \verb@%O@ & octal \\ #\verb@%t@ & mantissa to base 10 \\ #\verb@%l@ & mantissa to base of current logscale \\ #\verb@%s@ & mantissa to base of current logscale; scientific power \\ #\verb@%T@ & power to base 10 \\ #\verb@%L@ & power to base of current logscale \\ #\verb@%S@ & scientific power \\ #\verb@%c@ & character replacement for scientific power \\ #\verb@%b@ & mantissa of ISO/IEC 80000 notation (ki, Mi, Gi, Ti, Pi, Ei, Zi, Yi) \\ #\verb@%B@ & prefix of ISO/IEC 80000 notation (ki, Mi, Gi, Ti, Pi, Ei, Zi, Yi) \\ #\verb@%P@ & multiple of pi \\ %c l . %Format@Explanation %_ %%f@floating point notation %%e or %E@exponential notation; an "e" or "E" before the power %%g or %G@the shorter of %e (or %E) and %f %%h or %H@like %g with "x10^{%S}" or "*10^{%S}" instead of "e%S" %%x or %X@hex %%o or %O@octal %%t@mantissa to base 10 %%l@mantissa to base of current logscale %%s@mantissa to base of current logscale; scientific power %%T@power to base 10 %%L@power to base of current logscale %%S@scientific power %%c@character replacement for scientific power %%b@mantissa of ISO/IEC 80000 notation (ki, Mi, Gi, Ti, Pi, Ei, Zi, Yi) %%B@prefix of ISO/IEC 80000 notation (ki, Mi, Gi, Ti, Pi, Ei, Zi, Yi) %%P@multiple of pi @end table ^ ^^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^

Format Explanation
%f floating point notation
%e or %E exponential notation; an "e" or "E" before the power
%g or %G the shorter of %e (or %E) and %f
%h or %H %g with "x10^{%S}" or "*10^{%S}" instead of "e%S"
%x or %X hex
%o or %O octal
%t mantissa to base 10
%l mantissa to base of current logscale
%s mantissa to base of current logscale; scientific power
%T power to base 10
%L power to base of current logscale
%S scientific power
%c character replacement for scientific power
%b mantissa of ISO/IEC 80000 notation (ki, Mi, Gi, Ti, Pi, Ei, Zi, Yi)
%B prefix of ISO/IEC 80000 notation (ki, Mi, Gi, Ti, Pi, Ei, Zi, Yi)
%P multiple of π
A 'scientific' power is one such that the exponent is a multiple of three. Character replacement of scientific powers (`"%c"`) has been implemented for powers in the range -18 to +18. For numbers outside of this range the format reverts to exponential. Other acceptable modifiers (which come after the "%" but before the format specifier) are "-", which left-justifies the number; "+", which forces all numbers to be explicitly signed; " " (a space), which makes positive numbers have a space in front of them where negative numbers have "-"; "#", which places a decimal point after floats that have only zeroes following the decimal point; a positive integer, which defines the field width; "0" (the digit, not the letter) immediately preceding the field width, which indicates that leading zeroes are to be used instead of leading blanks; and a decimal point followed by a non-negative integer, which defines the precision (the minimum number of digits of an integer, or the number of digits following the decimal point of a float). Some systems may not support all of these modifiers but may also support others; in case of doubt, check the appropriate documentation and then experiment. Examples: set format y "%t"; set ytics (5,10) # "5.0" and "1.0" set format y "%s"; set ytics (500,1000) # "500" and "1.0" set format y "%+-12.3f"; set ytics(12345) # "+12345.000 " set format y "%.2t*10^%+03T"; set ytic(12345)# "1.23*10^+04" set format y "%s*10^{%S}"; set ytic(12345) # "12.345*10^{3}" set format y "%s %cg"; set ytic(12345) # "12.345 kg" set format y "%.0P pi"; set ytic(6.283185) # "2 pi" set format y "%.0f%%"; set ytic(50) # "50%" set log y 2; set format y '%l'; set ytics (1,2,3) #displays "1.0", "1.0" and "1.5" (since 3 is 1.5 * 2^1) There are some problem cases that arise when numbers like 9.999 are printed with a format that requires both rounding and a power. If the data type for the axis is time/date, the format string must contain valid codes for the 'strftime' function (outside of `gnuplot`, type "man strftime"). See `set timefmt` for a list of the allowed input format codes. 4 time/date specifiers ?commands set format date_specifiers ?commands set format time_specifiers ?set format date_specifiers ?set format time_specifiers ?set date_specifiers ?set time_specifiers ?date_specifiers ?time_specifiers There are two groups of time format specifiers: time/date and relative time. These may be used to generate axis tic labels or to encode time in a string. See `set xtics time`, `strftime`, `strptime`. The time/date formats are @start table - first is interactive cleartext form Format Explanation %a short name of day of the week (ignored on input) %A full name of day of the week (ignored on input) %b or %h abbreviated name of the month %B full name of the month %d day of the month, 01--31 %D shorthand for "%m/%d/%y" (only output) %F shorthand for "%Y-%m-%d" (only output) %k hour, 0--23 (one or two digits) %H hour, 00--23 (always two digits) %l hour, 1--12 (one or two digits) %I hour, 01--12 (always two digits) %j day of the year, 001--366 %m month, 01--12 %M minute, 00--60 %p "am" or "pm" %r shorthand for "%I:%M:%S %p" (only output) %R shorthand for "%H:%M" (only output) %s number of seconds since the start of year 1970 %S second, integer 00--60 on output, (double) on input %T shorthand for "%H:%M:%S" (only output) %U week of the year (CDC/MMWR "epi week") (ignored on input) %w day of the week, 0--6 (Sunday = 0) (ignored on input) %W week of the year (ISO 8601 week date) (ignored on input) %y year, 0-68 for 2000-2068, 69-99 for 1969-1999 %Y year, 4-digit %z timezone, [+-]hh:mm %Z timezone name, ignored string #\begin{tabular}{|cl|} \hline #\multicolumn{2}{|c|}{Date Specifiers}\\ #\hline \hline #Format & Explanation \\ \hline #\verb@%a@ & abbreviated name of day of the week \\ #\verb@%A@ & full name of day of the week \\ #\verb@%b@ or \verb@%h@ & abbreviated name of the month \\ #\verb@%B@ & full name of the month \\ #\verb@%d@ & day of the month, 01--31 \\ #\verb@%D@ & shorthand for \verb@"%m/%d/%y"@ (only output) \\ #\verb@%F@ & shorthand for \verb@"%Y-%m-%d"@ (only output) \\ #\verb@%k@ & hour, 0--23 (one or two digits)\\ #\verb@%H@ & hour, 00--23 (always two digits)\\ #\verb@%l@ & hour, 1--12 (one or two digits)\\ #\verb@%I@ & hour, 01--12 (always two digits)\\ #\verb@%j@ & day of the year, 001--366 \\ #\verb@%m@ & month, 01--12 \\ #\verb@%M@ & minute, 00--60 \\ #\verb@%p@ & "am" or "pm" \\ #\verb@%r@ & shorthand for \verb@"%I:%M:%S %p"@ (only output)\\ #\verb@%R@ & shorthand for \verb@%H:%M"@ (only output)\\ #\verb@%S@ & second, integer 00--60 on output, (double) on input\\ #\verb@%s@ & number of seconds since start of year 1970 \\ #\verb@%T@ & shorthand for \verb@"%H:%M:%S"@ (only output)\\ #\verb@%U@ & week of the year (CDC/MMWR "epi week") (ignored on input)\\ #\verb@%w@ & day of the week, 0--6 (Sunday = 0) \\ #\verb@%W@ & week of the year (ISO 8601 week date) (ignored on input)\\ #\verb@%y@ & year, 0-99 in range 1969-2068\\ #\verb@%Y@ & year, 4-digit \\ #\verb@%z@ & timezone, [+-]hh:mm \\ #\verb@%Z@ & timezone name, ignored string \\ %c l . %Format@Explanation %_ %%a@abbreviated name of day of the week %%A@full name of day of the week %%b or %h@abbreviated name of the month %%B@full name of the month %%d@day of the month, 01--31 %%D@shorthand for "%m/%d/%y" (only output) %%F@shorthand for "%Y-%m-%d" (only output) %%k@hour, 0--23 (one or two digits) %%H@hour, 00--23 (always two digits) %%l@hour, 1--12 (one or two digits) %%I@hour, 01--12 (always two digits) %%j@day of the year, 1--366 %%m@month, 01--12 %%M@minute, 0--60 %%p@"am" or "pm" %%r@shorthand for "%I:%M:%S %p" (only output) %%R@shorthand for %H:%M" (only output) %%S@second, integer 0--60 on output, (double) on input %%s@number of seconds since start of year 1970 %%T@shorthand for "%H:%M:%S" (only output) %%U@week of the year (CDC/MMWR "epi week") %%w@day of the week, 0--6 (Sunday = 0) %%W@week of the year (ISO 8601 week date) %%y@year, 0-99 in range 1969-2068 %%Y@year, 4-digit %%z@timezone, [+-]hh:mm %%Z@timezone name, ignored string @end table ^ ^^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^

Date Format Explanation
%a abbreviated name of day of the week
%A full name of day of the week
%b or %h abbreviated name of the month
%B full name of the month
%d day of the month, 01–31
%D shorthand for %m/%d/%y (only output)
%F shorthand for %Y-%m-%d (only output)
%k hour, 0–23 (one or two digits)
%H hour, 00–23 (always two digits)
%l hour, 1–12 (one or two digits)
%I hour, 01–12 (always two digits)
%j day of the year, 1–366
%m month, 01–12
%M minute, 0–60
%p "am" or "pm"
%r shorthand for %I:%M:%S %p (only output)
%R shorthand for %H:%M (only output)
%S second, integer 0–60 on output, (double) on input
%s number of seconds since start of year 1970
%T shorthand for %H:%M:%S (only output)
%U week of the year (CDC/MMWR "epi week")
%w day of the week, 0–6 (Sunday = 0)
%W week of the year (ISO 8601 week date)
%y year, 0-99 in range 1969-2068
%Y year, 4-digit
%z timezone, [+-]hh:mm
%Z timezone name, ignored string
For more information on the %W format (ISO week of year) see `tm_week`. The %U format (CDC/MMWR epidemiological week) is similar to %W except that it uses weeks that start on Sunday rather than Monday. Caveat: Both the %W and the %U formats were unreliable in gnuplot versions prior to 5.4.2. See unit test "week_date.dem". The relative time formats express the length of a time interval on either side of a zero time point. The relative time formats are @start table - first is interactive cleartext form Format Explanation %tD +/- days relative to time=0 %tH +/- hours relative to time=0 (does not wrap at 24) %tM +/- minutes relative to time=0 %tS +/- seconds associated with previous tH or tM field #\begin{tabular}{|cl|} \hline #\multicolumn{2}{|c|}{Time Specifiers}\\ #\hline \hline #Format & Explanation \\ \hline #\verb@%tD@ & +/- days relative to time=0 \\ #\verb@%tH@ & +/- hours relative to time=0 (does not wrap at 24) \\ #\verb@%tM@ & +/- minutes relative to time=0 \\ #\verb@%tS@ & +/- seconds associated with previous tH or tM field \\ %c l . %Format@Explanation %_ %%tD@+/- days relative to time=0 %%tH@+/- hours relative to time=0 (does not wrap at 24) %%tM@+/- minutes relative to time=0 %%tS@+/- seconds associated with previous tH or tM field @end table ^ ^^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^ ^

Time Format Explanation
%tD +/- days relative to time=0
%tH +/- hours relative to time=0 (does not wrap at 24)
%tM +/- minutes relative to time=0
%tS +/- seconds associated with previous tH or tM field
Numerical formats may be preceded by a "0" ("zero") to pad the field with leading zeroes, and preceded by a positive digit to define the minimum field width. The %S, and %t formats also accept a precision specifier so that fractional hours/minutes/seconds can be written. 5 Examples ?commands set format date_specifiers examples ?commands set format time_specifiers examples ?set format date_specifiers examples ?set format time_specifiers examples ?set date_specifiers examples ?set time_specifiers examples ?date_specifiers examples ?time_specifiers examples Examples of date format: Suppose the x value in seconds corresponds a time slightly before midnight on 25 Dec 1976. The text printed for a tic label at this position would be set format x # defaults to "12/25/76 \n 23:11" set format x "%A, %d %b %Y" # "Saturday, 25 Dec 1976" set format x "%r %D" # "11:11:11 pm 12/25/76" set xtics time format "%B" # "December" Examples of time format: The date format specifiers encode a time in seconds as a clock time on a particular day. So hours run only from 0-23, minutes from 0-59, and negative values correspond to dates prior to the epoch (1-Jan-1970). In order to report a time value in seconds as some number of hours/minutes/seconds relative to a time 0, use time formats %tH %tM %tS. To report a value of -3672.50 seconds set format x # default date format "12/31/69 \n 22:58" set format x "%tH:%tM:%tS" # "-01:01:12" set format x "%.2tH hours" # "-1.02 hours" set format x "%tM:%.2tS" # "-61:12.50" 3 grid ?commands set grid ?commands unset grid ?commands show grid ?set grid ?set grid vertical ?unset grid ?show grid ?grid The `set grid` command allows grid lines to be drawn on the plot. Syntax: set grid {{no}{m}xtics} {{no}{m}ytics} {{no}{m}ztics} {{no}{m}x2tics} {{no}{m}y2tics} {{no}{m}rtics} {{no}{m}cbtics} {polar {}} {layerdefault | front | back} {{no}vertical} { {, }} unset grid show grid The grid can be enabled and disabled for the major and/or minor tic marks on any axis, and the linetype and linewidth can be specified for major and minor grid lines, also via a predefined linestyle, as far as the active terminal driver supports this (see `set style line`). A polar grid can be drawn for 2D plots. This is the default action of `set grid` if the program is already in polar mode, but can be enabled explicitly by `set grid polar rtics` whether or not the program is in polar mode. Circles are drawn to intersect major and/or minor tics along the r axis, and radial lines are drawn with a spacing of . Tic marks around the perimeter are controlled by `set ttics`, but these do not produce radial grid lines. The pertinent tics must be enabled before `set grid` can draw them; `gnuplot` will quietly ignore instructions to draw grid lines at non-existent tics, but they will appear if the tics are subsequently enabled. If no linetype is specified for the minor gridlines, the same linetype as the major gridlines is used. The default polar angle is 30 degrees. If `front` is given, the grid is drawn on top of the graphed data. If `back` is given, the grid is drawn underneath the graphed data. Using `front` will prevent the grid from being obscured by dense data. The default setup, `layerdefault`, is equivalent to `back` for 2D plots. In 3D plots the default is to split up the grid and the graph box into two layers: one behind, the other in front of the plotted data and functions. Since `hidden3d` mode does its own sorting, it ignores all grid drawing order options and passes the grid lines through the hidden line removal machinery instead. These options actually affect not only the grid, but also the lines output by `set border` and the various ticmarks (see `set xtics`). In 3D plots grid lines at x- and y- axis tic positions are by default drawn only on the base plane parallel to z=0. The `vertical` keyword activates drawing grid lines in the xz and yz planes also, running from zmin to zmax. Z grid lines are drawn on the bottom of the plot. This looks better if a partial box is drawn around the plot---see `set border`. 3 hidden3d ?commands set hidden3d ?commands unset hidden3d ?commands show hidden3d ?set hidden3d ?unset hidden3d ?show hidden3d ?hidden3d ?nohidden3d The `set hidden3d` command enables hidden line removal for surface plotting (see `splot`). Some optional features of the underlying algorithm can also be controlled using this command. Syntax: set hidden3d {defaults} | { {front|back} {{offset } | {nooffset}} {trianglepattern } {{undefined } | {noundefined}} {{no}altdiagonal} {{no}bentover} } unset hidden3d show hidden3d In contrast to the usual display in gnuplot, hidden line removal actually treats the given function or data grids as real surfaces that can't be seen through, so plot elements behind the surface will be hidden by it. For this to work, the surface needs to have 'grid structure' (see `splot datafile` about this), and it has to be drawn `with lines` or `with linespoints`. When `hidden3d` is set, both the hidden portion of the surface and possibly its contours drawn on the base (see `set contour`) as well as the grid will be hidden. Each surface has its hidden parts removed with respect to itself and to other surfaces, if more than one surface is plotted. Contours drawn on the surface (`set contour surface`) don't work. `hidden3d` also affects 3D plotting styles `points`, `labels`, `vectors`, and `impulses` even if no surface is present in the graph. Unobscured portions of each vector are drawn as line segments (no arrowheads). Individual plots within the graph may be explicitly excluded from this processing by appending the extra option `nohidden3d` to the `with` specifier. Hidden3d does not affect solid surfaces drawn using the pm3d mode. To achieve a similar effect purely for pm3d surfaces, use instead `set pm3d depthorder`. To mix pm3d surfaces with normal `hidden3d` processing, use the option `set hidden3d front` to force all elements included in hidden3d processing to be drawn after any remaining plot elements, including the pm3d surface. Functions are evaluated at isoline intersections. The algorithm interpolates linearly between function points or data points when determining the visible line segments. This means that the appearance of a function may be different when plotted with `hidden3d` than when plotted with `nohidden3d` because in the latter case functions are evaluated at each sample. Please see `set samples` and `set isosamples` for discussion of the difference. The algorithm used to remove the hidden parts of the surfaces has some additional features controllable by this command. Specifying `defaults` will set them all to their default settings, as detailed below. If `defaults` is not given, only explicitly specified options will be influenced: all others will keep their previous values, so you can turn on/off hidden line removal via `set {no}hidden3d`, without modifying the set of options you chose. The first option, `offset`, influences the linetype used for lines on the 'back' side. Normally, they are drawn in a linetype one index number higher than the one used for the front, to make the two sides of the surface distinguishable. You can specify a different linetype offset to add instead of the default 1, by `offset `. Option `nooffset` stands for `offset 0`, making the two sides of the surface use the same linetype. Next comes the option `trianglepattern `. must be a number between 0 and 7, interpreted as a bit pattern. Each bit determines the visibility of one edge of the triangles each surface is split up into. Bit 0 is for the 'horizontal' edges of the grid, Bit 1 for the 'vertical' ones, and Bit 2 for the diagonals that split each cell of the original grid into two triangles. The default pattern is 3, making all horizontal and vertical lines visible, but not the diagonals. You may want to choose 7 to see those diagonals as well. The `undefined ` option lets you decide what the algorithm is to do with data points that are undefined (missing data, or undefined function values), or exceed the given x-, y- or z-ranges. Such points can either be plotted nevertheless, or taken out of the input data set. All surface elements touching a point that is taken out will be taken out as well, thus creating a hole in the surface. If = 3, equivalent to option `noundefined`, no points will be thrown away at all. This may produce all kinds of problems elsewhere, so you should avoid this. = 2 will throw away undefined points, but keep the out-of-range ones. = 1, the default, will get rid of out-of-range points as well. By specifying `noaltdiagonal`, you can override the default handling of a special case can occur if `undefined` is active (i.e. is not 3). Each cell of the grid-structured input surface will be divided in two triangles along one of its diagonals. Normally, all these diagonals have the same orientation relative to the grid. If exactly one of the four cell corners is excluded by the `undefined` handler, and this is on the usual diagonal, both triangles will be excluded. However if the default setting of `altdiagonal` is active, the other diagonal will be chosen for this cell instead, minimizing the size of the hole in the surface. The `bentover` option controls what happens to another special case, this time in conjunction with the `trianglepattern`. For rather crumply surfaces, it can happen that the two triangles a surface cell is divided into are seen from opposite sides (i.e. the original quadrangle is 'bent over'), as illustrated in the following ASCII art: C----B original quadrangle: A--B displayed quadrangle: |\ | ("set view 0,0") | /| ("set view 75,75" perhaps) | \ | |/ | | \ | C--D | \| A D If the diagonal edges of the surface cells aren't generally made visible by bit 2 of the there, the edge CB above wouldn't be drawn at all, normally, making the resulting display hard to understand. Therefore, the default option of `bentover` will turn it visible in this case. If you don't want that, you may choose `nobentover` instead. D hidden 6 See also ^ hidden line removal demo (hidden.dem) ^ and ^ complex hidden line demo (singulr.dem). ^ 3 history ?commands set history ?set history Syntax: set history {size } {quiet|numbers} {full|trim} {default} A log of recent gnuplot commands is kept by default in $HOME/.gnuplot_history. If this file is not found and xdg desktop support is enabled, the program will instead use $XDG_STATE_HOME/gnuplot_history. When leaving gnuplot the value of history size limits the number of lines saved to the history file. `set history size -1` allows an unlimited number of lines to be written to the history file. By default the `history` command prints a line number in front of each command. `history quiet` suppresses the number for this command only. `set history quiet` suppresses numbers for all future `history` commands. The `trim` option reduces the number of duplicate lines in the history list by removing earlier instances of the current command. Default settings: `set history size 500 numbers trim`. 3 isosamples ?commands set isosamples ?commands show isosamples ?set isosamples ?show isosamples ?isosamples The isoline density (grid) for plotting functions as surfaces may be changed by the `set isosamples` command. Syntax: set isosamples {,} show isosamples Each function surface plot will have iso-u lines and iso-v lines. If you only specify , will be set to the same value as . By default, sampling is set to 10 isolines per u or v axis. A higher sampling rate will produce more accurate plots, but will take longer. These parameters have no effect on data file plotting. An isoline is a curve parameterized by one of the surface parameters while the other surface parameter is fixed. Isolines provide a simple means to display a surface. By fixing the u parameter of surface s(u,v), the iso-u lines of the form c(v) = s(u0,v) are produced, and by fixing the v parameter, the iso-v lines of the form c(u) = s(u,v0) are produced. When a function surface plot is being done without the removal of hidden lines, `set samples` controls the number of points sampled along each isoline; see `set samples` and `set hidden3d`. The contour algorithm assumes that a function sample occurs at each isoline intersection, so change in `samples` as well as `isosamples` may be desired when changing the resolution of a function surface/contour. 3 isosurface ?commands set isosurface ?commands show isosurface ?set isosurface ?show isosurface Syntax: set isosurface {mixed|triangles} set isosurface {no}insidecolor Surfaces plotted by the command `splot $voxelgrid with isosurface` are by default constructed from a mixture of quadrangles and triangles. The use of quadrangles creates a less complicated visual impression. This command provides an option to tessellate with only triangles. By default the inside of an isosurface is drawn in a separate color. The method of choosing that color is the same as for hidden3d surfaces, where an offset is added to the base linetype. To draw both the inside and outside surfaces in the same color, use `set isosurface noinsidecolor`. 3 isotropic ?commands set isotropic ?set isotropic ?isotropic Syntax: set isotropic unset isotropic `set isotropic` adjusts the aspect ratio and size of the plot so that the unit length along the x, y, and z axes is the same. It is equivalent to `set size ratio -1; set view equal xyz` and supersedes both of those commands. This affects both 2D and 3D plots. `unset isotropic` relaxes both the 2D and 3D constraints. It is equivalent to the older commands `set size noratio; set view noequal_axes` but hopefully easier to remember. 3 jitter ?commands set jitter ?set jitter ?jitter =beeswarm Syntax: set jitter {overlap } {spread } {wrap } {swarm|square|vertical} Examples: set jitter # jitter points within 1 character width set jitter overlap 1.5 # jitter points within 1.5 character width set jitter over 1.5 spread 0.5 # same but half the displacement on x When one or both coordinates of a data set are restricted to discrete values then many points may lie exactly on top of each other. Jittering introduces an offset to the coordinates of these superimposed points that spreads them into a cluster. The threshold value for treating the points as being overlapped may be specified in character widths or any of the usual coordinate options. See `coordinates`. Jitter affects 2D plot styles `with points` and `with impulses`. It also affects 3D plotting of voxel grids. The default jittering operation displaces points only along x. This produces a distinctive pattern sometimes called a "bee swarm plot". The optional keyword `square` adjusts the y coordinate of displaced points in addition to their x coordinate so that the points lie in distinct layers separated by at least the `overlap` distance. To jitter along y (only) rather than along x, use keyword `vertical`. The maximum displacement (in character units) can be limited using the `wrap` keyword. Note that both the overlap criterion and the magnitude of jitter default to one character unit. Thus the plot appearance will change with the terminal font size, canvas size, or zoom factor. To avoid this you can specify the overlap criterion in the y axis coordinate system (the `first` keyword) and adjust the point size and spread multiplier as appropriate. See `coordinates`, `pointsize`. Caveat: jitter is incompatible with "pointsize variable". `set jitter` is also useful in 3D plots of voxel data. Because voxel grids are regular lattices of evenly spaced points, many view angles cause points to overlap and/or generate MoirÃ© patterns. These artifacts can be removed by displacing the symbol drawn at each grid point by a random amount. 3 key ?commands set key ?commands unset key ?commands show key ?set key ?unset key ?show key ?key ?nokey ?legend The `set key` command enables a key (or legend) containing a title and a sample (line, point, box) for each plot in the graph. The key may be turned off by requesting `set key off` or `unset key`. Individual key entries may be turned off by using the `notitle` keyword in the corresponding plot command. The text of the titles is controlled by the `set key autotitle` option or by the `title` keyword of individual `plot` and `splot` commands. See `key placement` for syntax of options that affect where the key is placed. #TeX \\ See `key layout` for syntax of options that affect the content of the key. Syntax (global options): set key {on|off} {default} {font ","} {{no}enhanced} {{no}title "" {}} {{no}autotitle {columnheader}} {{no}box {}} {{no}opaque {fc }} {width } {height } unset key By default the key is placed in the upper right inside corner of the graph. The optional `font` becomes the default for all elements of the key. You can provide an option title for the key as a whole that spans the full width of the key at the top. This title can use different font, color, justification, and enhancement from individual plot titles. Each component in a plot command is represented in the key by a single line containing corresponding title text and a line or symbol or shape representing the plot style. The title text may be auto-generated or given explicitly in the plot command as `title "text"`. Using the keyword `notitle` in the plot command will suppress generation of the entire line. If you want to suppress the text only, use `title ""` in the plot command. Contour plots generated additional entries in the key (see `cntrlabel`). You can add extra lines to the key by inserting a dummy plot command that uses the keyword `keyentry` rather than a filename or a function. See `keyentry`. A box can be drawn around the key (`box {...}`) with user-specified line properties. The `height` and `width` increments (specified in character units) are added to or subtracted from the size of the key box. This is useful mainly when you want larger borders around the key entries. By default the key is built up one plot at a time. That is, the key symbol and title are drawn at the same time as the corresponding plot. That means newer plots may sometimes place elements on top of the key. `set key opaque` causes the key to be generated after all the plots. In this case the key area is filled with background color or the requested fill color and then the key symbols and titles are written. The default can be restored by `set key noopaque`. The text in the key uses `enhanced` mode by default. This can be suppressed by the `noenhanced` keyword applied to the entire key, to the key title only, or to individual plot titles. `set key default` restores the default key configuration. set key notitle set key nobox noopaque set key fixed right top vertical Right noreverse enhanced autotitle set key noinvert samplen 4 spacing 1 width 0 height 0 set key maxcolumns 0 maxrows 0 4 3D key ?set key 3D ?set key splot ?key 3D ?key splot ?set key fixed ?key fixed Placement of the key for 3D plots (`splot`) by default uses the `fixed` option. This is very similar to `inside` placement with one important difference. The plot boundaries of a 3D plot change as the view point is rotated or scaled. If the key is positioned `inside` these boundaries then the key also moves when the view is changed. `fixed` positioning ignores changes to the view angles or scaling; i.e. the key remains fixed in one location on the canvas as the plot is rotated. For 2D plots the `fixed` option is exactly equivalent to `inside`. If `splot` is being used to draw contours, by default a separate key entry is generated for each contour level with a distinct line type. To modify this see `set cntrlabel`. 4 key examples ?set key examples ?key examples This places the key at the default location: set key default This places a key at a specific place (upper right) on the screen: set key at screen 0.85, 0.85 This places the key below the graph and minimizes the vertical space taken: set key below horizontal This places the key in the bottom left corner of the plot, left-justifies the text, gives the key box a title at the top, and draws a box around it with a thick border: set key left bottom Left title 'Legend' box lw 3 4 extra key entries ?key entries ?keyentry Ffigure_keyentry Normally each plot autogenerates a single line entry in the key. If you need more control over what appears in the key you can use the `keyentry` keyword in the `plot` or `splot` command to insert extra lines. Instead of providing a filename or function to plot, use `keyentry` as a placeholder followed by plot style information (used to generate a key symbol) and a title. All the usual options for title font, text color, `at` coordinates, and enhanced text markup apply. Example: set key outside right center title "Outcomes" plot $HEATMAP matrix with image notitle, \ keyentry with boxes fc palette cb 0 title "no effect", \ keyentry with boxes fc palette cb 1 title "threshold", \ keyentry with boxes fc palette cb 3 title "typical range", \ keyentry with labels nopoint title "as reported in [12]", \ keyentry with boxes fc palette cb 5 title "strong effect" 4 key autotitle ?commands set key autotitle ?set key autotitle ?key autotitle ?autotitle ?autotitle columnheader ?key autotitle columnheader `set key autotitle` causes each plot to be identified in the key by the name of the data file or function used in the plot command. This is the default. `set key noautotitle` disables the automatic generation of plot titles. =columnheader The command `set key autotitle columnheader` causes the first entry in each column of input data to be interpreted as a text string and used as a title for the corresponding plot. If the quantity being plotted is a function of data from several columns, gnuplot may be confused as to which column to draw the title from. In this case it is necessary to specify the column explicitly in the plot command, e.g. plot "datafile" using (($2+$3)/$4) title columnhead(3) with lines Note: The effect of `set key autotitle columnheader`, treatment of the first line in a data file as column headers rather than data applies even if the key is disabled by `unset key`. It also applies to `stats` and `fit` commands even though they generate no key. If you want the first line of data to be treated as column headers but _not_ to use them for plot titles, use `set datafile columnheaders`. In all cases an explicit `title` or `notitle` keyword in the plot command itself will override the default from `set key autotitle`. 4 key layout ?set key layout ?key layout Key layout options: set key {vertical | horizontal} {maxcols { | auto}} {maxrows { | auto}} {columns } {keywidth [screen|graph] } {Left | Right} {{no}reverse} {{no}invert} {samplen } {spacing } {width } {height } {title {""} {{no}enhanced} {center | left | right}} {font ","} {textcolor } Automatic arrangement of elements within the key into rows and columns is affected by the keywords shown above. The default is `vertical`, for which the key uses the fewest columns possible. Elements are aligned in a column until there is no more vertical space, at which point a new column is started. The vertical space may be limited using 'maxrows'. In the case of `horizontal`, the key instead uses the fewest rows possible. The horizontal space may be limited using 'maxcols'. The auto-selected number of rows and columns may be unsatisfactory. You can specify a definite number of columns using `set key columns `. In this case you may need to adjust the sample widths (`samplen`) and the total key width (`keywidth`). By default the first plot label is at the top of the key and successive labels are entered below it. The `invert` option causes the first label to be placed at the bottom of the key, with successive labels entered above it. This option is useful to force the vertical ordering of labels in the key to match the order of box types in a stacked histogram. `set key title "text"` places an overall title at the top of the key. Font, text justification, and other text properties specific to the title can be specified by placing the required keywords immediately after the `"text"` in this command. Font or text properties specified elsewhere apply to all text in the key. The default layout places a style sample (color, line, point, shape, etc) at the left of the key entry line, and the title text at the right. The text and sample positions can be swapped using the `reverse` keyword. Text justification of the individual plot titles within the key is controlled by `Left` or `Right` (default). The horizontal extend of the style sample can be set to an approximate number of character width (`samplen`). When using the TeX/LaTeX group of terminals or terminals in which formatting information is embedded in the string, `gnuplot` is bad at estimating the amount of space required, so the automatic key layout may be poor. If the key is to be positioned at the left, it may help to use the combination `set key left Left reverse` and force the appropriate number of columns or total key width. 4 key placement ?commands set key placement ?set key placement ?key placement Key placement options: set key {inside | outside | fixed} {lmargin | rmargin | tmargin | bmargin} {at }} {left | right | center} {top | bottom | center} {offset ,} This section describes placement of the primary, auto-generated key. To construct a secondary key or place plot titles elsewhere, see `multiple keys`. #TeX \begin{minipage}{0.5\textwidth} To understand positioning, the best concept is to think of a region, i.e., inside/outside, or one of the margins. Along with the region, keywords `left/center/right` (l/c/r) and `top/center/bottom` (t/c/b) control where within the particular region the key should be placed. In `inside` mode, the keywords `left` (l), `right` (r), `top` (t), `bottom` (b), and `center` (c) push the key out toward the plot boundary as illustrated here: #TeX \end{minipage} #TeX \hspace{0.15\textwidth} #TeX \begin{minipage}{0.35\textwidth} t/l t/c t/r c/l c c/r b/l b/c b/r #TeX \end{minipage} In `outside` mode, automatic placement is similar to the above illustration, but with respect to the view, rather than the graph boundary. That is, a border is moved inward to make room for the key outside of the plotting area, although this may interfere with other labels and may cause an error on some devices. The particular plot border that is moved depends upon the position described above and the stacking direction. For options centered in one of the dimensions, there is no ambiguity about which border to move. For the corners, when the stack direction is `vertical`, the left or right border is moved inward appropriately. When the stack direction is `horizontal`, the top or bottom border is moved inward appropriately. #TeX \begin{minipage}{0.5\textwidth} The margin syntax allows automatic placement of key regardless of stack direction. When one of the margins `lmargin` (lm), `rmargin` (rm), `tmargin` (tm), and `bmargin` (bm) is combined with a single, non-conflicting direction keyword, the key is positioned along the outside of the page as shown here. Keywords `above` and `over` are synonymous with `tmargin`. Keywords `below` and `under` are synonymous with `bmargin`. #TeX \end{minipage} #TeX \hspace{0.1\textwidth} #TeX \begin{minipage}{0.4\textwidth} l/tm c/tm r/tm t/lm t/rm c/lm c/rm b/lm b/rm l/bm c/bm r/bm #TeX \end{minipage} For version compatibility, `above`, `over`, `below`, or `under` without any additional l/c/r or stack direction keyword uses `center` and `horizontal`. The keyword `outside` without any additional t/b/c or stack direction keyword uses `top`, `right` and `vertical` (i.e., the same as t/rm above). The can be a simple x,y,z as in previous versions, but these can be preceded by one of five keywords (`first`, `second`, `graph`, `screen`, `character`) which selects the coordinate system in which the position of the first sample line is specified. See `coordinates` for more details. The effect of `left`, `right`, `top`, `bottom`, and `center` when is given is to align the key as though it were text positioned using the label command, i.e., `left` means left align with key to the right of , etc. 4 key offset ?commands set key offset ?set key offset ?key offset Regardless of the key placement options chosen, the final position of the key can be adjusted manually by specifying an offset. As usual, the x and y components of the offset may be given in character, graph, or screen coordinates. 4 key samples ?commands set key samples ?set key samples ?key samples By default, each plot on the graph generates a corresponding entry in the key. This entry contains a plot title and a sample line/point/box of the same color and fill properties as used in the plot itself. The font and textcolor properties control the appearance of the individual plot titles that appear in the key. Setting the textcolor to "variable" causes the text for each key entry to be the same color as the line or fill color for that plot. This was the default in some earlier versions of gnuplot. The length of the sample line can be controlled by `samplen`. The sample length is computed as the sum of the tic length and times the character width. It also affects the positions of point samples in the key since these are drawn at the midpoint of the sample line, even if the line itself is not drawn. Key entry lines are single-spaced based on the current font size. This can be adjusted by `set key spacing `. The is a number of character widths to be added to or subtracted from the length of the string. This is useful only when you are putting a box around the key and you are using control characters in the text. `gnuplot` simply counts the number of characters in the string when computing the box width; this allows you to correct it. 4 multiple keys ?multiple keys ?set key multiple keys ?key multiple keys =legend Ffigure_multiple_keys It is possible to construct a legend/key manually rather than having the plot titles all appear in the auto-generated key. This allows, for example, creating a single legend for the component panels in a multiplot. set multiplot layout 3,2 columnsfirst set style data boxes plot $D using 0:6 lt 1 title at 0.75, 0.20 plot $D using 0:12 lt 2 title at 0.75, 0.17 plot $D using 0:13 lt 3 title at 0.75, 0.14 plot $D using 0:14 lt 4 title at 0.75, 0.11 set label 1 at screen 0.75, screen 0.22 "Custom combined key area" plot $D using 0:($6+$12+$13+$14) with linespoints title "total" unset multiplot 3 label ?commands set label ?commands unset label ?commands show label ?set label ?unset label ?show label ?label ?nolabel Arbitrary labels can be placed on the plot using the `set label` command. Syntax: set label {} {""} {at } {left | center | right} {norotate | rotate {by }} {font "{,}"} {noenhanced} {front | back} {textcolor } {point | nopoint} {offset } {nobox} {boxed {bs }} {hypertext} unset label {} show label The is specified by either x,y or x,y,z, and may be preceded by `first`, `second`, `polar`, `graph`, `screen`, or `character` to indicate the coordinate system. See `coordinates` for details. The tag is an integer that is used to identify the label. If no is given, the lowest unused tag value is assigned automatically. The tag can be used to delete or modify a specific label. To change any attribute of an existing label, use the `set label` command with the appropriate tag, and specify the parts of the label to be changed. The can be a string constant, a string variable, or a string- valued expression. See `strings`, `sprintf`, and `gprintf`. By default, the text is placed flush left against the point x,y,z. To adjust the way the label is positioned with respect to the point x,y,z, add the justification parameter, which may be `left`, `right` or `center`, indicating that the point is to be at the left, right or center of the text. Labels outside the plotted boundaries are permitted but may interfere with axis labels or other text. Some terminals support enclosing the label in a box. See `set style textbox`. Not all terminals can handle boxes for rotated text. If `rotate` is given, the label is written vertically. If `rotate by ` is given, the baseline of the text will be set to the specified angle. Some terminals do not support text rotation. Font and its size can be chosen explicitly by `font "{,}"` if the terminal supports font settings. Otherwise the default font of the terminal will be used. Normally the enhanced text mode string interpretation, if enabled for the current terminal, is applied to all text strings including label text. The `noenhanced` property can be used to exempt a specific label from the enhanced text mode processing. The can be useful if the label contains underscores, for example. See `enhanced text`. If `front` is given, the label is written on top of the graphed data. If `back` is given (the default), the label is written underneath the graphed data. Using `front` will prevent a label from being obscured by dense data. `textcolor ` changes the color of the label text. can be a linetype, an rgb color, or a palette mapping. See help for `colorspec` and `palette`. `textcolor` may be abbreviated `tc`. `tc default` resets the text color to its default state. `tc lt ` sets the text color to that of line type . `tc ls ` sets the text color to that of line style . `tc palette z` selects a palette color corresponding to the label z position. `tc palette cb ` selects a color corresponding to on the colorbox. `tc palette fraction `, with 0<=val<=1, selects a color corresponding to the mapping [0:1] to grays/colors of the `palette`. `tc rgb "#RRGGBB"` or `tc rgb "0xRRGGBB"` sets an arbitrary 24-bit RGB color. `tc rgb 0xRRGGBB` As above; a hexadecimal constant does not require quotes. If a is given, using keywords `lt`, `pt` and `ps`, see `style`, a point with the given style and color of the given line type is plotted at the label position and the text of the label is displaced slightly. This option is used by default for placing labels in `mouse` enhanced terminals. Use `nopoint` to turn off the drawing of a point near the label (this is the default). The displacement defaults to 1,1 in `pointsize` units if a is given, 0,0 if no is given. The displacement can be controlled by the optional `offset ` where is specified by either x,y or x,y,z, and may be preceded by `first`, `second`, `graph`, `screen`, or `character` to select the coordinate system. See `coordinates` for details. If one (or more) axis is timeseries, the appropriate coordinate should be given as a quoted time string according to the `timefmt` format string. See `set xdata` and `set timefmt`. The options available for `set label` are also available for the `labels` plot style. See `labels`. In this case the properties `textcolor`, `rotate`, and `pointsize` may be followed by keyword `variable` rather than by a fixed value. In this case the corresponding property of individual labels is determined by additional columns in the `using` specifier. 4 examples ?label examples ?set label examples Examples: To set a label at (1,2) to "y=x", use: set label "y=x" at 1,2 To set a Sigma of size 24, from the Symbol font set, at the center of the graph, use: set label "S" at graph 0.5,0.5 center font "Symbol,24" To set a label "y=x^2" with the right of the text at (2,3,4), and tag the label as number 3, use: set label 3 "y=x^2" at 2,3,4 right To change the preceding label to center justification, use: set label 3 center To delete label number 2, use: unset label 2 To delete all labels, use: unset label To show all labels (in tag order), use: show label To set a label on a graph with a timeseries on the x axis, use, for example: set timefmt "%d/%m/%y,%H:%M" set label "Harvest" at "25/8/93",1 To display a freshly fitted parameter on the plot with the data and the fitted function, do this after the `fit`, but before the `plot`: set label sprintf("a = %3.5g",par_a) at 30,15 bfit = gprintf("b = %s*10^%S",par_b) set label bfit at 30,20 To display a function definition along with its fitted parameters, use: f(x)=a+b*x fit f(x) 'datafile' via a,b set label GPFUN_f at graph .05,.95 set label sprintf("a = %g", a) at graph .05,.90 set label sprintf("b = %g", b) at graph .05,.85 To set a label displaced a little bit from a small point: set label 'origin' at 0,0 point lt 1 pt 2 ps 3 offset 1,-1 To set a label whose color matches the z value (in this case 5.5) of some point on a 3D splot colored using pm3d: set label 'text' at 0,0,5.5 tc palette z 4 hypertext ?hypertext ?label hypertext ?set label hypertext Some terminals (wxt, qt, svg, canvas, win) allow you to attach hypertext to specific points on the graph or elsewhere on the canvas. When the mouse hovers over the anchor point, a pop-up box containing the text is displayed. Terminals that do not support hypertext will display nothing. You must enable the `point` attribute of the label in order for the hypertext to be anchored. Enhanced text markup is not applied to hypertext labels. Examples: set label at 0,0 "Plot origin" hypertext point pt 1 plot 'data' using 1:2:0 with labels hypertext point pt 7 \ title 'mouse over point to see its order in data set' # mousing over any point of this pm3d surface will display # its Z coordinate as hypertext splot '++' using 1:2:(F($1,$2)) with pm3d, \ '++' using 1:2:(F($1,$2)):(sprintf("%.3f", F($1,$2))) with labels \ hypertext point lc rgb "0xff000000" notitle For the wxt and qt terminals, left-click on a hypertext anchor after the text has appeared will copy the hypertext to the clipboard. ^
^ ^ click to see hypertext demo ^
EXPERIMENTAL (implementation details may change) - Text of the form "image{,}:{\n}" will trigger display of the image file in a pop-up box. The optional size overrides a default box size 300x200. The types of image file recognized may vary by terminal type, but *.png should always work. Any additional text lines following the image filename are displayed as usual for hypertext. Example: set label 7 "image:../figures/Fig7_inset.png\nFigure 7 caption..." set label 7 at 10,100 hypertext point pt 7 3 linetype ?commands set linetype ?commands show linetype ?set linetype ?show linetype The `set linetype` command allows you to redefine the basic linetypes used for plots. The command options are identical to those for "set style line". Unlike line styles, redefinitions by `set linetype` are persistent. They are not affected by `reset`. However the initial linetype properties are restored by `reset session`. For example, whatever linetypes one and two look like to begin with, if you redefine them like this: set linetype 1 lw 2 lc rgb "blue" pointtype 6 set linetype 2 lw 2 lc rgb "forest-green" pointtype 8 everywhere that uses lt 1 will now get a thick blue line. This includes uses such as the definition of a temporary linestyle derived from the base linetype 1. Similarly lt 2 will now produce a thick green line. This mechanism can be used to define a set of personal preferences for the sequence of lines used in gnuplot. The recommended way to do this is to add to the run-time initialization file ~/.gnuplot a sequence of commands like set linetype 1 lc rgb "dark-violet" lw 2 pt 1 set linetype 2 lc rgb "sea-green" lw 2 pt 7 set linetype 3 lc rgb "cyan" lw 2 pt 6 pi -1 set linetype 4 lc rgb "dark-red" lw 2 pt 5 pi -1 set linetype 5 lc rgb "blue" lw 2 pt 8 set linetype 6 lc rgb "dark-orange" lw 2 pt 3 set linetype 7 lc rgb "black" lw 2 pt 11 set linetype 8 lc rgb "goldenrod" lw 2 set linetype cycle 8 Every time you run gnuplot the line types will be initialized to these values. You may initialize as many linetypes as you like. If you do not redefine, say, linetype 3 then it will continue to have the default properties (in this case blue, pt 3, lw 1, etc). Similar script files can be used to define theme-based color choices, or sets of colors optimized for a particular plot type or output device. =cycle The command `set linetype cycle 8` tells gnuplot to re-use these definitions for the color and linewidth of higher-numbered linetypes. That is, linetypes 9-16, 17-24, and so on will use this same sequence of colors and widths. The point properties (pointtype, pointsize, pointinterval) are not affected by this command. `unset linetype cycle` disables this feature. If the line properties of a higher numbered linetype are explicitly defined, this takes precedence over the recycled low-number linetype properties. 3 link ?commands set link ?set link ?link Syntax: set link {x2 | y2} {via inverse } unset link The `set link` command establishes a mapping between the x and x2 axes, or the y and y2 axes. maps primary axis coordinates onto the secondary axis. maps secondary axis coordinates onto the primary axis. Examples: set link x2 This is the simplest form of the command. It forces the x2 axis to have identically the same range, scale, and direction as the x axis. Commands `set xrange`, `set x2range`, `set auto x`, etc will affect both the x and x2 axes. set link x2 via x**2 inverse sqrt(x) plot "sqrt_data" using 1:2 axes x2y1, "linear_data" using 1:2 axes x1y1 This command establishes forward and reverse mapping between the x and x2 axes. The forward mapping is used to generate x2 tic labels and x2 mouse coordinate The reverse mapping is used to plot coordinates given in the x2 coordinate system. Note that the mapping as given is valid only for x non-negative. When mapping to the y2 axis, both and must use y as dummy variable. 3 lmargin ?commands set lmargin ?set lmargin ?lmargin The command `set lmargin` sets the size of the left margin. Please see `set margin` for details. 3 loadpath ?commands set loadpath ?commands show loadpath ?set loadpath ?show loadpath ?loadpath The `loadpath` setting defines additional locations for data and command files searched by the `call`, `load`, `plot` and `splot` commands. If a file cannot be found in the current directory, the directories in `loadpath` are tried. Syntax: set loadpath {"pathlist1" {"pathlist2"...}} show loadpath Path names may be entered as single directory names, or as a list of path names separated by a platform-specific path separator, eg. colon (':') on Unix, semicolon (';') on DOS/Windows/OS/2 platforms. The `show loadpath`, `save` and `save set` commands replace the platform-specific separator with a space character (' '). If the environment variable GNUPLOT_LIB is set, its contents are appended to `loadpath`. However, `show loadpath` prints the contents of `set loadpath` and GNUPLOT_LIB separately. Also, the `save` and `save set` commands ignore the contents of GNUPLOT_LIB. 3 locale ?commands set locale ?set locale ?locale The `locale` setting determines the language with which `{x,y,z}{d,m}tics` will write the days and months. Syntax: set locale {""} may be any language designation acceptable to your installation. See your system documentation for the available options. The command `set locale ""` will try to determine the locale from the LC_TIME, LC_ALL, or LANG environment variables. To change the decimal point locale, see `set decimalsign`. To change the character encoding to the current locale, see `set encoding`. 3 logscale ?commands set logscale ?commands unset logscale ?commands show logscale ?set logscale ?unset logscale ?show logscale ?set log ?logscale ?nologscale Syntax: set logscale {} unset logscale show logscale where may be any combinations of `x`, `x2`, `y`, `y2`, `z`, `cb`, and `r` in any order. is the base of the log scaling (default is base 10). If no axes are specified, the command affects all axes except `r`. The command `unset logscale` turns off log scaling for all axes. Note that the ticmarks generated for logscaled axes are not uniformly spaced. See `set xtics`. Examples: To enable log scaling in both x and z axes: set logscale xz To enable scaling log base 2 of the y axis: set logscale y 2 To enable z and color log axes for a pm3d plot: set logscale zcb To disable z axis log scaling: unset logscale z 3 macros ?commands set macros ?set macros In this version of gnuplot macro substitution is always enabled. Tokens in the command line of the form @ will be replaced by the text string contained in . See `substitution`. 3 mapping ?commands set mapping ?commands show mapping ?set mapping ?show mapping ?mapping If data are provided to `splot` in spherical or cylindrical coordinates, the `set mapping` command should be used to instruct `gnuplot` how to interpret them. Syntax: set mapping {cartesian | spherical | cylindrical} A cartesian coordinate system is used by default. For a spherical coordinate system, the data occupy two or three columns (or `using` entries). The first two are interpreted as the azimuthal and polar angles theta and phi (or "longitude" and "latitude"), in the units specified by `set angles`. The radius r is taken from the third column if there is one, or is set to unity if there is no third column. The mapping is: x = r * cos(theta) * cos(phi) y = r * sin(theta) * cos(phi) z = r * sin(phi) Note that this is a "geographic" spherical system, rather than a "polar" one (that is, phi is measured from the equator, rather than the pole). For a cylindrical coordinate system, the data again occupy two or three columns. The first two are interpreted as theta (in the units specified by `set angles`) and z. The radius is either taken from the third column or set to unity, as in the spherical case. The mapping is: x = r * cos(theta) y = r * sin(theta) z = z The effects of `mapping` can be duplicated with the `using` specifier of the `splot` command, but `mapping` may be more convenient if many data files are to be processed. However even if `mapping` is used, `using` may still be necessary if the data in the file are not in the required order. `mapping` has no effect on `plot`. ^ See also ^ world.dem: mapping demos. ^ 3 margin ?commands set margins ?commands show margins ?set margin ?set margins ?show margins ?margins The `margin` is the distance between the plot border and the outer edge of the canvas. The size of the margin is chosen automatically, but can be overridden by the `set margin` commands. `show margin` shows the current settings. To alter the distance between the inside of the plot border and the data in the plot itself, see `set offsets`. Syntax: set lmargin {{at screen} } set rmargin {{at screen} } set tmargin {{at screen} } set bmargin {{at screen} } set margins